Renormalization-group study of weakly first-order phase transitions

a r X i v :h e p -p h /0610277v 1 21 O c t 2006SLAC-PUB-12168TU-778October,2006Possible Signals of Wino LSP at the Large Hadron Collider M.Ibe 1,Takeo Moroi 2and T.T.Yanagida 3,41Stanford Linear Accelerator Center,Stanford University,Stanford,CA943092Department of Physics,Tohoku University,Sendai,Japan 3Department of Physics,University of Tokyo,Tokyo 113-0033,Japan 4Research Center for the Early Universe,University of Tokyo,Tokyo 113-0033,JapanAbstractWe consider a class of anomaly-mediated supersymmetry breaking models wheregauginos acquire masses mostly from anomaly mediation while masses of other superparticles are from K¨a hler interactions,which are as large as gravitino mass ∼O (10−100)TeV.In this class of models,the neutral Wino becomes the lightest superparticle in a wide parameter region.The mass splitting between charged and neutral Winos are very small and experimental discovery of such Winos is highly non-trivial.We discuss how we should look for Wino-induced signals at Large Hadron Collider.1IntroductionIn the vacua of broken supersymmetry(SUSY)not only the gravitino but also squarks and sleptons acquire tree-level SUSY-breaking masses through supergravity(SUGRA) effects[1].On the other hand,if there is no singletfield in the hidden sector,quantum-loop corrections generate gaugino masses,which is often called as anomaly mediation[2,3]. This is the most economical mechanism for giving SUSY-breaking masses to all SUSY particles in the SUSY standard model(SSM)since it does not require any extrafield other than ones responsible for the SUSY breaking.In this model the gauginos are much lighter than the squarks and sleptons due to the loop effects.That is,there is a little disparity in the spectrum of SUSY particles.The masses of squarks and sleptons(and also that of the gravitino)are O(10−100)TeV for the gaugino masses less than O(1)TeV. Because of this disparity the anomaly mediation model is free from all problems in the SSM such asflavor-changing neutral current and CP problems[4].Furthermore,the mass of the lightest Higgs boson is naturally above the experimental lower bound m H>114.4 GeV[5].From the cosmological point of view,the gravitino-overproduction problem[6] in the early universe is much less serious in the above model due to the relatively large gravitino mass.It is also notable that a consistent scenario of thermal leptogenesis[7]is possible in the present scheme[8],and that the lightest superparticle(LSP),which is the neutral Wino,can be a good candidate for the dark matter in the universe[9,10].The purpose of this paper is to discuss possible tests of the above anomaly mediation model at the Large Hadron Collider(LHC)experiments.The crucial point is that the charged and neutral Winos are the most-motivated LSPs whose masses almost degenerate with each other,and the neutral Wino˜W0is slightly lighter than the charged one˜W±[11].In a cosmological scenario[10],a sizable amount of Winos are produced by the decay of gravitino originating from inflaton decay[12],and provided that such Wino can be the dark matter in the universe,the mass of the Wino is predicted as M2≃100GeV−2TeV.Therefore,it is highly possible that the Wino is within the reach of the LHC.1Unfortunately,however,it is also possible that superparticles other than Winos can be hardly produced at the LHC,depending on the model parameters.Indeed,as we will see,the gluino-Wino mass ratio M3/M2can be larger than the prediction of the pure anomaly mediation model,M3/M2≃8.Thus,it is difficult to produce the gluinos atthe LHC except for very optimistic cases as well as sfermions.Therefore it is now highly important to discuss signals of the Wino production at the LHC.2Properties of WinosWefirst discuss the mass spectrum of superparticles.We assume that the masses of squarks,sleptons and Higgs bosons are dominantly from SUGRA effects.With a generic K¨a hler potential,all the scalar bosons except the lightest Higgs boson acquire SUSY breaking masses of the order of the gravitino mass(m3/2).For the gaugino masses,on the contrary,tree-level SUGRA contributions are extremely suppressed if there is no singlet elementaryfield in the hidden sector.In this paper,we adopt the above setup and consider the situation that the scalar masses(as well as the gravitino mass)are of the order of O(10−100)TeV while gauginos are much lighter.In addition,we also assume that Higgsinos and heavy Higgs bosons have masses of O(10−100)TeV.Hereafter,we call such a scenario as“no singlet scenario”.If there is no singletfield in the hidden sector,effects of anomaly mediation becomes very important in generating gaugino masses[2,3].At Q∼m3/2(with Q being a renormalization scale),anomaly-mediation contributions to the gaugino masses are given byM(AMSB) a =−b a g2amass in the“no singlet scenario”.Indeed,we expect the following K¨a hler potential:K∋cH u H d+c′M2G,(4) where F X is the vacuum expectation value of the F-component of X.Thus,µ-and B-parameters are both of O(m3/2)and they are independent.For the successful electro-weak symmetry breaking,one linear combination of Higgs bosons should become light: with the so-calledβ-parameter,the(standard-model-like)light doublet is denoted as sinβH u−cosβH∗d,where H u and H d are up-and down-type Higgs bosons,respectively.Then,threshold corrections to the gaugino masses from the Higgs-Higgsino loop are given by[3,15]∆M(Higgs)1=316π2L,(5)∆M(Higgs)2=g22|µ|2−m2A ln|µ|22We assume that the vacuum expectation value of X is much smaller than M G.Figure1:Gaugino masses as functions of L/m3/2for a real value of L.The Wino mass is given in the solid line,while the dotted and dashed lines are for Bino and gluinomasses,respectively.Here we take m3/2=50TeV.The cancellation of the Wino mass for L/m3/2≃−1is a result of our specific choice of the phase,Arg(L)=π.For a generic phase of L,the cancellation becomes milder,though the Wino mass can be much lighterthan M(AMSB)2for|L/m3/2|≃1and Arg(L)∼π.Theµ-parameter(and L)is a complex variable and the Wino and Bino masses depend on the relative phase betweenµand m3/2.(Here,we use the bases where the gravitinomass is real and positive.)Importantly,with a distractive interference between M(AMSB)2and∆M(Higgs)2,the Wino mass can be even smaller than the purely anomaly mediated one.As an example,in Fig.1,we plot the gaugino masses for m3/2=50TeV as functions of L/m3/2,assuming that L is real for simplicity.In this case,we see that the threshold corrections drastically change the gaugino mass and even cancel the anomaly mediatedWino mass.In our analysis,gaugino masses are given by M a=M(AMSB)a +∆M(Higgs)aatQ=m3/2,and we take into account the effects of renormalization group evolutions below this scale.We have checked that the ratios of two gaugino masses are insensitive to the gravitino mass for a given L/m3/2.A wide variety of gaugino mass in the“no singlet scenario”has strong implications forcollider physics.In the pure anomaly mediation,all the gaugino masses are determined only by the gravitino mass and corresponding gauge coupling constants as shown in Eq.(1),and hence a negative search for gluino-induced signals results in lower bounds on other gaugino masses,in particular,that of Wino mass.In the“no singlet scenario”, on the contrary,gluino and Wino masses are independent.Thus,even if gluino-induced signals will not be found at the LHC,we will still have a strong motivation to look for Wino-induced signals for the parameter region where Wino is relatively light.In the pure anomaly mediation model,the lightest gaugino is always the Wino.How-ever,in the“no singlet scenario”,the Wino LSP is not a generic consequence any more since the Bino may become lighter than Wino.However,Fig.1shows that Wino becomes the LSP if|L/m3/2|is less than a few,which is the case when|µ|and m A are both fairlyclose to the gravitino mass.In addition,the Wino LSP scenario can never cease from being the most motivated scenario from the point of view of cosmology.This is because the Bino LSP results in the overclosure of the universe[3].Therefore,in this paper,we concentrate on the Wino LSP scenario,where the lightest neutralino and the lightest chargino are both(almost)purely Winos.Now,we consider detailed properties of the Wino.As discussed in Ref.[11],the dominant mass splitting between the charged and neutral Winos comes from one-loop gauge boson contributions to the gaugino masses whenµis large.The splitting is given by∆M=m˜W±−m˜W0=g22πcos2θc f2π∆M3 1−m2πprocesses are a few%or smaller for M2>∼88GeV.3We also estimate the lifetime of charged Wino,which is given by O(10−10)sec.Then,charged Winos produced at the LHC travel typically O(1−10)cm before they decay.As we discuss in the following,this fact has very important consequences in the study of our scenario at the LHC.3Wino at the LHCNow we are at the position to discuss how we can test the“no singlet scenario”at the LHC.In studying superparticles at the LHC,it is often assumed that the productions of superparticles are mostly via productions of colored superparticles.Even though the primary superparticles are scalar quarks and/or gluino,they decay into various lighter superparticles which may be scalar leptons,charginos,and/or neutralinos.Of course, those processes are important when scalar quarks and/or gluino are not too heavy.Since we are interested in the case where all the sfermions(as well as heavy Higgs multiplets)have masses of order100TeV,they are irrelevant for the LHC.Hereafter,we will not consider the production of those particles.On the contrary,masses of gauginos(in particular,that of gluino)are of order100 GeV–1TeV.As discussed in the previous section,the gluino-to-Wino mass ratio is a free parameter in the“no singlet scenario”,since the prediction of pure anomaly mediation, which gives M3/M2≃8,can be significantly altered.For a given Wino mass M2,the discovery of SUSY at the LHC depends on the ratio M3/M2.When M3/M2is relatively small,the gluino is light enough so that a significant amount of gluino is produced at the LHC.In this case,the dominant production processes of superparticles are gluino pair productions.The primary gluinos decay into lighter super-particles and,at the end of decay chain,the neutral Winos are produced.Consequently, we observe events with energetic jets and large missing E T.In this case,signals from the production of superparticles are basically the same as those in well-studied SUSY models.Hereafter,we concentrate on a rather pessimistic case where the gluino mass is so largethat a gluino production rate is suppressed at the LHC.In this case,the only possibility of detecting superparticles is direct productions of charged and neutral Winos.(Notice that the Bino production cross section is very small since the scalar quarks are extremely heavy.)In our case,the neutral Wino is the LSP and hence is stable.Thus,even if it is produced at the LHC,it does not leave any consequence on the detector.The charged Wino is heavier than the neutral one and hence is unstable.The mass difference∆M= mW±−m W is expected to be160–170MeV,and the charged Wino mainly decays as ˜W±→˜W0π±with lifetime of O(10−10)sec.Thus,most of charged Winos decay beforeit reaches a muon detector.In addition,the emitted pion has very tiny energy;its boost factor is typicallyγπ∼O(1).Thus,it is challenging to identify such a low-energy pion. These facts make the discover of Wino production events very difficult.Winos can be pair-produced at the LHC via Drell-Yang processes q¯q→˜W+˜W−and q¯q′→˜W±˜W0.However,these events cannot be recorded since there is no trigger relevant for them.Indeed,in order for the event to be recorded,thefinal state should contain high energy jet(s)and/or high energy electro-magnetic activity.In the Drell-Yang process,we do not expect such activities since the charged Winos decay before reaching the muon detector.However,events may be recorded if Winos are produced with high E T jet(s).In particular,ATLAS[18]and CMS[19]both plan to trigger on missing E T events with energetic jets;if the transverse energy of the jet and missing E T are both larger than50–100GeV,events will be recorded.(Hereafter,we call such a trigger as J+XE trigger.) With pp collision at the LHC,a Wino pair can be produced in association with a high E T jet via the following parton-level processes:q¯q→˜W+˜W−g,gq→˜W+˜W−q,g¯q→˜W+˜W−¯q,(11)q¯q′→˜W±˜W0g,gq→˜W±˜W0q′,g¯q→˜W±˜W0¯q′.(12) Gluon and(anti-)quark in thefinal state are hadronized and become energetic jets.Thus, at the trigger level,this class of events are characterized by a high E T mono-jet,missingFigure2:Total cross section of a Wino pair+mono-jet production eventσ(pp→˜W+˜W−j)+σ(pp→˜W±˜W0j)at√4We have cross checked our results by using the codes,FeynArts[22]and FormCalc[23].of Tevatron[11].If the charged Wino travels O(10)cm or longer before it decays,it hits some of the detectors and the track from charged Wino may be reconstructed.The track from charged Wino may be also distinguished from tracks from other standard-model charged particles by using the time-of-flight information and/or by measuring ionization energy loss rate(dE/dx).In addition,it is important to note that,with the lifetime of O(10−10)sec,most of the charged Winos are likely to decay inside the detector.Then,we may observe tracks which disappear somewhere in the detector.This will be regarded as a spectacular signal of new physics beyond the standard model.In particular,in the ATLAS detector,the transition radiation tracker(TRT)will be implemented,which is located at56–107cm from the beam axis[20].The TRT continuously follows charged tracks.Thus,if the charged Wino decays inside the TRT,the charged Wino track will be identified by off-line analysis.In addition,with the TRT,charged pions emitted by the decays of˜W±may be also seen. Such events have very rare backgrounds and hence they can be used for the discovery of the Wino production.We calculate the cross section of the processes pp→˜W+˜W−j and pp→˜W±˜W0j,with the requirement that at least one charged Wino travels transverse length L T longer than L(min)before it decays.At the trigger level,no hadronic nor electro-magnetic activities Twill be identified except for the mono-jet,so the missing E T is equal to the transverse energy of the mono-jet.In order to use the J+XE trigger,we impose a cut such that E T≥100GeV for thefinal-state jet.L T is sensitive to the decay width of charged Wino. Since we consider the case where gauginos are the only light superparticles,we use Eq.(9)for∆M.The decay width of charged Wino is given in Eq.(10).Cross sections for several values of L(min)are shown in Fig.3.Assuming L∼100fb−1Tfor high luminosity run of the LHC,for example,a sizable number of charged Winos with L T∼O(10)cm will be produced.Thus,if we canfind their tracks,it will provide an intriguing signal which cannot be explained in the standard model.Requiring10events with L T≥50cm(1m)with L=100fb−1,for example,the LHC can cover M2≤350 GeV(200GeV).Thus,the search for(short)tracks of heavy charged particles is strongly√Figure3:Cross section of the process pp→˜W˜W j atprecision.In order to perform a statistical analysis of mono-jet+missing E T event,it is crucial to understand the total background cross section.As well as the process pp→Zj,other processes may contribute to the background.One of such is the process pp→ZZj if both Z’s decay invisibly.Thus,we have also calculated the cross section of this process. Taking account of the branching ratio of the invisible mode of Z,we have found that the background cross section from pp→ZZj is29–0.23fb for E T=100−500GeV, which is smaller than the signal cross section when the Wino mass is smaller than∼500 GeV.In addition,we will obtain some information about this class of backgrounds using leptonic decay modes of Z.Thus,we consider that the process pp→ZZj is not a serious background.The process pp→W±j followed by leptonic decay of W±may also give backgrounds if the charged lepton goes into the beam pipe.However,the probability of charged lepton escaping into the beam pipe may not be so large.In addition,the number of this type of backgrounds will be also estimated by studying mono-jet events with a single charged lepton and missing E T.We consider that cross sections of other processes resulting in the mono-jet+missing E Tfinal state are also small enough to be neglected.If the standard-model cross section of the mono-jet+missing E T event is understood precisely,an excess beyond the statistical error may be regarded as a signal of Wino+ mono-jet events.That is,the expected number of background events is O(107−104)forE T>100−500GeV of the mono-jet at a high luminosity L=100fb−1,for example. Then,the number of the Wino production events with a mono-jet becomes statistically significant when M2<∼400GeV(see Fig.2).It may be the case that the background cross section cannot be determined with such a high precision because of some systematic errors.We will not go into the detailed study of systematic error.Instead,we estimate how well the systematic error should be controlled tofind an anomaly;in order to cover the Wino mass of100,200,300,400,and500GeV, systematic error in the determination of background cross section should be smaller than>100GeV 1.9,0.28,0.083,0.032,and0.015%(12,4.2,1.8,0.87,and0.45%)for E(min)T(500GeV).Finally,let us briefly discuss what happens if Higgsino mass(i.e.,theµ-parameter)is smaller than∼TeV.So far,we have considered the case where superparticles other than gauginos are as heavy as O(100)TeV,and hence the mass difference between charged and neutral Winos is determined mainly by the radiative corrections from gauge-boson loops.In this case,∆M is given by Eq.(9)and the lifetime of charged Wino is more or less predicted.If theµ-parameter is smaller,on the contrary,∆M is affected by the gaugino-Higgsino mixing.In this case,∆M can be enhanced or suppressed,depending onµ-and other parameters.In particular,∆M becomes smaller than the pion mass and the lifetime of charged Wino becomes longer in some parameter region.In this case,it is much easier tofind tracks of the charged Wino since˜W±does not decay inside the detector.It should be also noticed here that such a charged Wino with the lifetime of O(10−8)sec may be used as a probe of deep interior of heavy nuclei[24].AcknowledgmentThe authors would like thank S.Asai,J.Kanzaki and T.Kobayashi for valuable dis-cussion and useful comments.M.I.is grateful to T.Hahn and C.Schappacher for kind explanation of FormCalc.This work was supported in part by the U.S.Department of Energy under contract number DE-AC02-76SF00515(M.I.)and by the Grant-in-Aid for Scientific Research from the Ministry of Education,Science,Sports,and Culture of Japan, No.15540247(T.M.)and14102004(T.T.Y.).References[1]H.P.Nilles,Phys.Rept.110(1984)1;S.P.Martin,arXiv:hep-ph/9709356.[2]L.Randall and R.Sundrum,Nucl.Phys.B557,79(1999).[3]G.F.Giudice,M.A.Luty,H.Murayama and R.Rattazzi,JHEP9812,027(1998).[4]F.Gabbiani,E.Gabrielli,A.Masiero and L.Silvestrini,Nucl.Phys.B477,321(1996).[5]W.M.Yao et al.[Particle Data Group],J.Phys.G33,1(2006).[6]S.Weinberg,Phys.Rev.Lett.48(1982)1303;See,for a recent work,K.Kohri,T.Moroi and A.Yotsuyanagi,Phys.Rev.D73(2006)123511,and references therein.[7]M.Fukugita and T.Yanagida,Phys.Lett.B174,45(1986);For a recent review,W.Buchmuller,R.D.Peccei and T.Yanagida,Ann.Rev.Nucl.Part.Sci.55,311 (2005).[8]M.Ibe,R.Kitano,H.Murayama and T.Yanagida,Phys.Rev.D70,075012(2004);M.Ibe,R.Kitano and H.Murayama,Phys.Rev.D71,075003(2005).[9]T.Moroi and L.Randall,Nucl.Phys.B570,455(2000).[10]M.Ibe,Y.Shinbara and T.T.Yanagida,arXiv:hep-ph/0608127.[11]J.L.Feng,T.Moroi,L.Randall,M.Strassler and S.f.Su,Phys.Rev.Lett.83,1731(1999).[12]M.Kawasaki, F.Takahashi and T.T.Yanagida,Phys.Lett.B638,8(2006);M.Kawasaki,F.Takahashi and T.T.Yanagida,Phys.Rev.D74,043519(2006);M.Endo,M.Kawasaki,F.Takahashi and T.T.Yanagida,arXiv:hep-ph/0607170.[13]J.D.Wells,Phys.Rev.D71,015013(2005).[14]K.Inoue,M.Kawasaki,M.Yamaguchi and T.Yanagida,Phys.Rev.D45,328(1992).[15]T.Gherghetta,G.F.Giudice and J.D.Wells,Nucl.Phys.B559,27(1999).[16]A.Heister et al.[ALEPH Collaboration],Phys.Lett.B533,223(2002).[17]S.D.Thomas and J.D.Wells,Phys.Rev.Lett.81,34(1998).[18]ATLAS homepage,http://atlas.web.cern.ch.[19]CMS homepage,http://cms.cern.ch.[20]ATLAS Collaboration,CERN-LHCC-97-16;CERN-LHCC-97-17.[21]J.Pumplin,D.R.Stump,J.Huston,i,P.Nadolsky and W.K.Tung,JHEP0207,012(2002).[22]T.Hahn,mun.140,418(2001).[23]T.Hahn and M.Perez-Victoria,mun.118,153(1999).[24]K.Hamaguchi,T.Hatsuda and T.T.Yanagida,arXiv:hep-ph/0607256.。

the critical study of languagenorman fairclough"Norman Fairclough's Critical Discourse Analysis: Language, Power, and Social Change" is a seminal work in the field of critical discourse analysis. In this book, Fairclough presents a framework for analyzing the relationship between language and power, arguing that language is not neutral but is instead used to shape and reproduce social relations and inequality.Fairclough's approach to critical discourse analysis emphasizes the importance of examining the context and history of a text, as well as the ways in which it is produced and consumed. He argues that language is not simply a tool for communication, but is instead a means of constructing and reproducing social reality. By analyzing the language used in different texts, we can gain insight into the ways in which power is exercised and contested in society.One of the key contributions of this book is Fairclough's development of the concept of "discourse practice," which refers to the ways in which language is used to create and maintain social structures and relations. He argues that discourse practices are shaped by broader social, political, and economic factors, and that they can have a profound impact on the way people think and behave.Overall, "The Critical Study of Language" is a must-read for anyone interested in the intersection of language, power, and social change. Fairclough's approach provides a framework for analyzing the ways in which language is used to reproduce inequality and for imagining alternative ways of using language to promote social justice.。

浅议小组活动在外语课堂教学中的重要性摘要：在二语习得（second language development）的研究领域，很多学者证明了合作型学习方式（collaborative learning）对于外语学习的重要性。

小组活动（group work）是实现学习者合作型学习的重要方式之一。

本文介绍了小组活动的外语教学实践意义，以及如何充分发挥小组活动在外语课堂中的积极作用的建议。

关键词：二语习得合作型学习方式小组活动西方大部分语言学家基本认为：“语言是用于人类交际的一种任意的、口语的、符号系统。

”（刘润清，2002：1）显然，语言是交际工具。

然而，在传统外语教学中，往往忽略学习者的外语交际，影响到学习者实际运用外语的交际能力的发展。

在二语习得教学方法的众多研究中，小组活动被认为是能够为学习者提供更多外语交际实践机会的课堂组织方式。

long和porter（1985）总结了小组活动对于二语习得的教学实践的五个积极意义：“小组活动能够竲加学习者外语语言实践的机会”（p208）；“小组活动能够促进提高学习者外语练习的质量”（p208）；“小组活动能够促进学生的外语自主学习”（p210）；“小组活动可以创造一个积极的，互助的外语学习环境”（p211）；“小组活动可以帮助提高学习者的外语学习动力”（p212）。

gibbons（2002）详细地讨论了小组活动的外语教学实践意义。

gibbons首先总结了三条mcgroarty在1993年对于小组活动有利于外语学习的讨论。

第一，小组活动可以让学习者获取更多的外语输入（input），而且这些输入的形式多样，因为每个组员都有自己表达外语的方式；第二，组员之间互相交流，其外语输出（output）也相应增多。

组员之间轮流地用外语交际，完成小组任务；虽然老师不在场，但是小组成员共同承担学习任务，他们实现了真正意义上的外语学习的自主与自我负责；第三，学习者交际的语言是有具体背景的（contextualized），这样的外语交际有明显的目的性，组员对交际内容更容易接受和理解（p17）。

教育硕士开题报告英文IntroductionEducation plays a crucial role in shaping the future of individuals, societies, and nations. As a result, the pursuit of advanced degrees in education, such as a Master's in Education, has become increasingly popular. This report aims to provide a comprehensive overview of the proposed research study for the Education Master's thesis.BackgroundTraditional teaching methods often fail to capture the attention and engage students effectively in the learning process. With the advancement of technology, schools have seen a shift towards integrating digital tools and resources into the classroom environment. This digital transformation has brought forth several benefits, including improved student engagement and enhanced learning outcomes. However, it is essential to evaluate the impact and effectiveness of these digital tools on education comprehensively.Research ProblemThe primary focus of this study is to investigate the impact of integrating digital tools, specifically interactive multimedia, in primary classrooms. The goal is to assess the effectiveness of these tools in enhancing student engagement, developing critical thinking skills, and improving academic performance. It is essential to understand the challenges and opportunities associatedwith implementing these digital tools to inform pedagogical practices and ensure successful integration into the classroom. Research Questions1. What is the impact of interactive multimedia tools on student engagement in primary classrooms?2. How do interactive multimedia tools contribute to the development of critical thinking skills in primary students?3. Do interactive multimedia tools improve academic performance in primary students?4. What challenges and opportunities arise from the implementation of interactive multimedia tools in primary classrooms?Research Objectives1. To evaluate the impact of interactive multimedia tools on student engagement in primary classrooms.2. To assess the contribution of interactive multimedia tools to the development of critical thinking skills.3. To examine the correlation between the use of interactive multimedia tools and academic performance in primary students.4. To identify the challenges and opportunities associated with implementing interactive multimedia tools in primary classrooms. Research MethodologyTo accomplish the research objectives, a mixed-methods approach will be employed. The study will involve both quantitative andqualitative data collection and analysis. Questionnaires will be administered to primary school teachers and students to measure student engagement, critical thinking skills, and academic performance. Additionally, interviews and focus groups will be conducted to gather qualitative data on the challenges and opportunities regarding the implementation of interactive multimedia tools in classrooms.Expected OutcomesBased on the analysis of the collected data, this study aims to provide insights into the effectiveness of integrating interactive multimedia tools in primary classrooms. It is anticipated that the research will demonstrate a positive impact on student engagement, critical thinking skills, and academic performance. Additionally, the study will identify potential challenges and opportunities to aid educators in effectively implementing these tools in their teaching practices.ConclusionWith the increasing prevalence of technology in education, it is crucial to evaluate the impact of digital tools, such as interactive multimedia, on primary students' educational experiences. Through this research, we hope to contribute to the knowledge base surrounding the integration of digital tools in classrooms and inform educators about the potential benefits and challenges associated with their implementation.。

研究方法如何在顶级管理学期刊发表论文（五）：方法与结果来源：南开管理评论一旦选择一个有趣而适当的选题，设计并执行一个合理的数据收集，制定一个引人注目的“伏笔”和发展一个坚实的理论，这些艰巨而又令人兴奋的工作完成后，人们就很容易坐视不前、麻痹放松，在各种方法和结果中游走。

接下来的工作似乎很简单直接，也许有点按部就班——向读者报告：（1）如何获得数据以及为什么获得数据；（2）如何分析数据以及发现了什么。

对于AMJ这一系列的关于如何在AMJ发表的叙述性文章，确实有许多读者在等待着它的出版。

因此，如果我们这篇文章缺乏说服力，我们希望它至少能提供一些信息。

作为作者，我们不得不承认，在写这些章节的时候，我们已经屈服于放松注意力的诱惑。

我们听到同事们说，他们把这些部分交给研究团队的初级成员，让他们在草稿写作中“练手”，好像这些部分的重要性不如开头部分、假设发展和讨论部分那么重要。

也许的确如此。

但作为过去两年来现任编辑团队的成员，我们面对这样一个现实：“方法”和“结果”部分，即使不是最关键的部分，也往往在审稿人如何评价稿件方面发挥着重要作用。

如果这些章节并没有对数据收集程序和结果提供清晰、详细的描述，反而常常让审稿人感到困惑，并会就作者使用的研究程序和发现，提出比他们回答更多的问题。

相比之下，一个有效的陈述可以对作者说服读者相信他们的理论论点（或其中的一部分）得到支持的程度产生至关重要的影响。

高质量的“方法”和“结果”部分也传达了表现作者责任心的积极信号。

知道他们在准备这些章节时是谨慎而严谨的，对于讨论是建议拒绝还是建议修改请求的外审来说可能会有所不同。

为了更好地理解审稿人共同关心的问题，我们在任期内对每一封被拒稿件的决定信进行了评估。

我们发现有几个问题在被拒绝的手稿中比在要求修改的手稿中出现的频率要高得多。

我们的评估结果，如果不令人惊讶的话，揭示了这两个部分的一系列非常一致的主要问题，我们总结为“三个度”（3C:Completeness，Clarity，Credibility）：完整度、清晰度和可信度。

群体研究的英语作文Title: The Importance and Benefits of Group Studies。

Introduction:Group studies refer to a collaborative learning approach where a group of individuals come together to study and discuss academic subjects or topics. This method has gained immense popularity due to its numerous advantages and benefits. In this essay, we will explore the significance of group studies and discuss the advantages it offers to students.Body:1. Enhanced Learning Experience:Group studies provide an enhanced learning experience as students can exchange ideas, clarify doubts, and gain a deeper understanding of the subject matter. Differentindividuals bring their unique perspectives, knowledge, and insights to the table, enriching the overall learning process. Through discussions and debates, students can challenge their own beliefs and broaden their horizons.2. Improved Problem-Solving Skills:Working in a group setting allows students to tackle complex problems collectively. Each member can contribute their thoughts and suggestions, leading to a comprehensive analysis of the problem. Group discussions foster critical thinking, creativity, and the ability to think outside the box. Students can learn from each other's problem-solving approaches and develop their own strategies.3. Effective Time Management:Group studies promote effective time management skills. By setting study schedules, dividing tasks, and adhering to deadlines, students learn to manage their time efficiently. The shared responsibility within the group ensures that each member remains accountable, leading to increasedproductivity and a sense of discipline.4. Enhanced Communication Skills:Participating in group studies helps students improve their communication skills. They learn to express their ideas clearly, listen actively to others, and engage in meaningful discussions. Through interactions with peers, students gain confidence in public speaking, develop effective listening skills, and learn to articulate their thoughts concisely.5. Increased Motivation and Support:Studying alone can sometimes be demotivating and isolating. Group studies provide a supportive environment where students can motivate and encourage each other. The collective effort and shared goals create a sense of camaraderie, boosting individual motivation. Additionally, group members can provide academic support, share resources, and help each other overcome challenges.6. Preparation for Real-World Collaboration:In the professional world, collaboration and teamwork are essential skills. Group studies prepare students for future endeavors by familiarizing them with collaborative work dynamics. They learn to work harmoniously with diverse individuals, respect different opinions, and develop essential teamwork skills such as leadership, cooperation, and compromise.Conclusion:Group studies offer numerous advantages and benefits to students, including an enhanced learning experience, improved problem-solving skills, effective time management, enhanced communication skills, increased motivation and support, and preparation for real-world collaboration. By engaging in group studies, students can maximize their academic potential, develop crucial life skills, and foster a sense of community and cooperation. Therefore, it is highly recommended for students to actively participate in group studies to reap the rewards it offers.。

哈尔滨工业大学工程硕士学位论文AbstractThe 7N01 aluminum alloy used in high-speed train is one of Al-Zn-Mg high strengthaluminum alloy and it will generate large welding residual stress after welding. Theexistence of residual stress will lead adverse affect to the performance of the structure.Vibration stress relief(VSR) is a new method to eliminate residual stress, which is simple,portable, energy-saving, environment-friendly, efficient and safe. It has been widely usedin ferrous metal to eliminate welding residual stress.For high-strength aluminum alloys, because the welding residual stress is far fromthe yield strength of the material, the conventional vibration stress relief treatment haveno obvious effect on eliminating welding residual stress. In this paper, combined with thestudy of vibration stress relief of 7N01 aluminum alloy, thermal-vibration stressrelief(TVSR) treatment is proposed. By combining the theoretical analysis andexperimental research, the effects of temperature of thermal-vibration stress relief on theelimination of welding residual stress and the effect of thermal-vibration stress relief onthe mechanical properties and microstructure of the material were studied.Based on the principle of vibration stress relief and the aging process of aluminumalloy, a thermal-vibration stress relief platform was built. First,the mechanism of VSRwas analyzed from the macroscopic and microscopic perspectives, and a VSR platformthat satisfies the experimental requirements was set up. Then three kinds of heatingmethods, including welding residual heat, flame and heating belt, were explored. Finally,a ceramic heating belt system with temperature feedback was selected. Combiningtheoretical analysis and experimental investigation, the selection principle of VSRparameters is proposed.The influence of temperature on the effect of TVSR to eliminate residual stress wasstudied. First,with the increase of temperature, the strength of the material decreased, andit has decreased significantly from 100 to 200 °C. Then the aging precipitation of 7N01 aluminum alloy was studied. The precipitation temperature of 7N01 aluminum alloyaging strengthening phase was in the range of 120-170 °C. The welding joints weresubjected to comparative experiments at different temperatures. After Thermal vibrationstress relief treatment at 25 °C (room temperature), 100 °C, 150 °C, and 200 °residual stress decreased by 38.3%, 50.7%, 60.0%, and 74.0%, respectively. Withincreasing temperature in the range of 100-200 °C, the effect of eliminating residual stress was better.Thermal-vibration stress relief treatment of 7N01 aluminum alloy large welded哈尔滨工业大学工程硕士学位论文structural parts was conducted to study the effects of thermal-vibration stress relief on the properties and microstructure of the materials. After thermal-vibration stress relief treatment, the tensile strength of the joints is improved, the hardness and fatigue properties remain basically unchanged, and the bending and stress corrosion resistance of the materials are still good. The microstructure of the welded joints is clearly refined, the micro dislocation density increases, the distribution is even, and a large number of dislocation tangles occur, which is consistent with the increase in the strength of the material.Finally, the TVSR treatment and VSR treatment were applied to the actual structure of the bolster. The peak residual stress after Thermal vibration stress relief treatment decreased by 50.3% on average, while the peak residual stress after vibration stress relief treatment decreased by 28.5% on average. The results show that the Thermal vibration stress relief is more significant than the vibration stress relief to eliminate the welding residual stress. The thermal-vibration stress relief technology put forward by this groupis the development of thermal-vibration stress relief technology. It has important guiding value in practical engineering applications and has broad application prospects.Keywords: thermal-vibration stress relief，7N01 aluminum alloy，welding residual stress，mechanism study，dislocation slip哈尔滨工业大学工程硕士学位论文目录I 摘要............................................................................................................................II Abstract .........................................................................................................................1第1章绪论................................................................................................................1 1.1研究背景及意义..................................................................................................1.2焊接残余应力的产生及调控 (2)1.2.1焊接残余应力的产生 (2)1.2.2焊接残余应力的调控 (2)1.2.3工程中消除残余应力方法 (5)1.3热振时效新技术的研究现状 (6)1.3.1振动时效的机理研究 (6)1.3.2振动时效对材料性能和组织的影响 (9)1.3.3热振时效新技术的研究现状 (10)1.4本文主要的研究内容和方法 (11)12第2章实验材料及测试............................................................................................2.1实验材料及焊接参数........................................................................................1212 2.2测量残余应力的方法........................................................................................2.2.1残余应力测量方法简述 (12)2.2.2超声波法测残余应力 (13)15 2.3焊接接头力学性能测试....................................................................................2.3.1焊接接头硬度测试 (15)2.3.2焊接接头静拉伸测试 (16)2.3.3焊接接头疲劳性能测试 (17)2.3.4焊接接头耐应力腐蚀性能测试 (17)18 2.4焊接接头微观组织表征....................................................................................2.4.1焊接接头金相显微组织观察 (18)2.4.2焊接接头透射电镜观察 (19)19 2.5本章小结............................................................................................................ 第3章热振时效系统的搭建及振动参数分析.. (20)哈尔滨工业大学工程硕士学位论文20 3.1热振时效系统搭建............................................................................................3.1.1振动时效系统搭建 (20)3.1.2加热系统特点及选择 (22)3.1.3热振时效实验方法 (22)23 3.2振动时效参数的确定........................................................................................233.2.1激振力 .........................................................................................................243.2.2激振时间 .....................................................................................................243.2.3激振频率 .....................................................................................................25 3.3热振时效效果评价............................................................................................26 3.4本章小结............................................................................................................ 第4章热振时效理论及温度探究. (27)27 4.1热振时效的理论分析........................................................................................4.1.1热振时效方法的提出 (27)4.1.2热振时效可行性分析 (27)4.1.3温度对7N01合金时效析出行为的影响 (29)4.2不同温度的热振时效实验探究 (30)304.2.1温度探究实验 .............................................................................................314.2.2实验结果分析 .............................................................................................4.2.3温度的选择及分析 (34)4.3大型结构件热振时效实验 (35)4.3.1热振时效处理 .............................................................................................354.3.2残余应力结果对比 (37)394.3.3实验结果分析 .............................................................................................40 4.4本章小结............................................................................................................ 第5章热振时效对焊接接头的影响. (41)5.1热振时效对接头性能的影响 (41)5.1.1对接头硬度的影响 (41)5.1.2对接头拉伸性能的影响 (43)5.1.3对接头疲劳性能的影响 (45)5.1.4对接头耐应力腐蚀性能的影响 (49)5.2热振时效对焊接接头组织影响 (51)515.2.1金相组织观察 .............................................................................................哈尔滨工业大学工程硕士学位论文525.2.2透射电镜观察 .............................................................................................5.2.3热振时效微观机理分析 (54)54 5.3本章小结............................................................................................................ 第6章热振时效在高速列车枕梁结构中的应用.. (56)56 6.1高速列车枕梁结构............................................................................................56 6.2枕梁结构热振时效实验....................................................................................57 6.3残余应力结果分析............................................................................................61 6.4本章小结............................................................................................................62结论..........................................................................................................................64参考文献...................................................................................................................... 哈尔滨工业大学学位论文原创性声明和使用权限.. (68)69致谢..........................................................................................................................。

自我控制的能量模型:证据、质疑和展望＊高科李琼黄希庭【摘要】摘要:自我控制的能量模型是解释自我控制的一个重要理论模型。

该模型认为，所有的自我控制行为依赖一种共同且有限的能量，执行自我控制会消耗这种能量，导致自我损耗效应的产生，但能量也可以通过一些方法得以恢复和提升。

该模型得到大量行为和生理层面研究的支持，但也有研究者从疲劳、情绪、动机、血糖指标、时间知觉等方面提出质疑。

未来研究可从自我能量的性质、总量等角度进一步完善能量模型，同时结合我国文化探讨理想、信念、价值观对提升我国国民意志力的作用。

【期刊名称】心理学探新【年(卷),期】2012(032)002【总页数】6【关键词】关键词:自我控制；能量模型；自我损耗；理想；信念；价值观【文献来源】https:///academic-journal-cn_psychological-exploration_thesis/020********.html自我控制(self－control)是人类特有的心理特征之一，研究自我控制是理解自我本质及其机制的关键(Baumeister，2009)。

20世纪70年代以前，自我控制一直是哲学、宗教、法学的研究范畴，并且常以意志(volition)作为其代名词。

之后心理学家也开始关注自我控制，20世纪80～90年代已经出现了不少考察该现象的实证研究。

当前对自我控制的心理学研究主要有三种取向:发展研究取向，着重探讨自我控制能力发展的年龄特征及其影响因素；人格研究取向，将自我控制视为一种稳定的人格特质，并来考察其内部机制；认知研究取向，认为自我控制是信念、期望、态度、意图的函数。

认知取向下的研究提出了一些有代表性的理论模型:例如，TOTE模型、双系统理论模型(hot－cold model)。

近年来出现了一种新的研究取向——自我控制的能量模型，该模型是基于TOTE模型提出的，自提出以来就备受关注，并得到了诸多研究的证实和发展。

a rXiv:c ond-ma t/965059v19May1996Weak first-order transition in the quasi-one-dimensional frustrated XY antiferromagnet M.L.Plumer Centre de Recherche en Physique du Solide et D´e partement de Physique Universit´e de Sherbrooke,Sherbrooke,Qu´e bec,Canada J1K 2R1A.Mailhot INRS-EAU,2800rue Einstein,C.P.7500,Ste.-Foy,Qu´e bec,Canada G1V 4C7(May 1996)Abstract The results of finite-size scaling analysis of histogram Monte-Carlo simula-tions on the stacked triangular XY antiferromagnet with anisotropic near-neighbor exchange interactions are presented.With ferromagnetic interplane coupling ten times stronger than the antiferromagnetic intraplane interaction (J /J ⊥=−10),a weak first-order transition is revealed.These results repre-sents the first simulational corroboration of a wide variety of renormalization-group calculations made over the past twenty years.As such,they shed lighton recent controversy regarding the critical behavior in this and similar frus-trated systems and have particular relevance to recently reported data onCsCuCl 3.75.40.Mg,75.40.Cx,75.10.HkTypeset using REVT E XAlthough the earliest,as well as the most recent,efforts using4−ǫrenormalization-group (RG)techniques to study the critical behvior in simple frustrated antiferromagnets(AF) indicated that these systems undergo afluctuation-inducedfirst order transition,a plethora of other recent studies have resulted in a wide variety of scenarios.The recent interest in thisfield has been inspired by the proposal of Kawamura of new chiral universality classes in the XY and Heisenberg cases based on his study of the4−ǫRG expansion as well as Monte Carlo(MC)simulations[1].This suggestion is in contrast with results from a 2+ǫRG expansion of the nonlinear sigma model(NLσ)from which either an O(4)(in the Heisenberg case),tricritical,orfirst-order,transition is expected[2].It is important to note that most of the critical exponents estimated by Kawamura are not so different from those expected at a mean-field tricritical transition.Although all subsequent MC work has been in support of Kawamura’s chiral universality for the Heisenberg system[3], nearly two years ago the present authors published the results of extensive MC simulations which gave strong support to the idea of tricriticality in the XY case[4].In that work (hereafter referred to as I),a simple hexagonal lattice was considered with AF exchange interactions in the triangular plane J⊥=1,giving rise to frustration,and ferromagnetic coupling along the c-axis,J =−1.This model thus represents isotropic near-neighbor couplings.It was also studied with the addition of an in-plane magneticfield H,where a weakfirst order transition was revealed to an unfrustated3-state Potts phase at small values of H[5](hereafter referred to as II).We report here MC simulation results for the XY model using J⊥=1and J =−10,which represents somewhat quasi-one-dimensional exchange anisotropy.Finite-size scaling of these new data show strong evidence of afirst-order transition at the ordering temperature but with a tendancy toward tricritical behavior at a slightly higher temperature.These results are consistent with very recent specific heat data on CsCuCl3[6].Relevant work published prior to1995is discussed in I,Ref.[7],and references therein. It is useful to review here the more recent results pertaining to the present study,beginning with those based on standard RG theory.Higher-order expansions in4−ǫhave reaffirmed re-sults from the earlier studies in support of afirst-order transition in both XY and Heisenberg cases[8].In contrast,a partial resummation based on the1/N expansion has been shown to yield a continuous transition for both models[9].The delicate nature of this model is further revealed by the very recent proposal of yet another newfixed point based on RG cal-culations[10].Detailed re-examinations of the NLσmodel have also given rise to a variety of scenarios.Azaria et al.[11]have demonstrated the existence of an additional length scale which may be relevant for the interpretation of MC results onfinite-size systems.In another study,this model has been shown to yield a variety of possibilities,including a two-step pro-cess(first proposed by Chubukov[12])where afirst order transition to a“nematic”phase is followed by a continuous transition to a chiral state as the temperature is lowered[13]. Although these results may be of relevance to the present work(see below),it should be emphasized that the validity of the NLσmodel of frustrated systems has been questioned [14]as,indeed,has the standard Ginsburg-Landau-Wilson approach[2,11].Other recent theoretical work includes the observation of a two-step transition process in a frustrtated two-dimensional model by MC simulations[15],criticality controlled by a Lifshitz point in helimagnets[16],as well as the possibility to investigate chirality using polarized neutrons [17].In addition to some recent review articles which summarize experimental estimates of critical exponents[18],several new results on specific materials have appeared[19,21,6]. Although many of these data support the existence of chiral universality,most do so only marginally and some data clearly suggest O(4)criticality or afirst order transition.Of particular relevance to the present work are the results on CsCuCl3[6],discussed in more detail below.As in I and II,the standard Metropolis MC algorithm was used in this work,along with analysis based on the histogram technique,on L×L×L lattices with L=12-33.However, because the exchange anisotropy causes a lower Metropolis acceptance rate,longer runs (typically by about a factor of two)were employed here,with thermodynamic averages per run calculated using1×106MC steps per spin(MCS)for the smaller lattices and2.5×106MCS for the larger lattices,after discarding the initial2×105–7×105MCS for thermalization.Averaging was then made over6(smaller L)to16(larger L)runs, giving4×107MCS for the calculation of averages with the larger lattices.Errors were then estimated by taking the standard deviation of results among the runs.A rough determination of the transition temperature wasfirst made by examination of various thermodynamic quantities in short-run temperature sweeps at L=24.From these results,the estimate T c≃4.6was made.Histograms were then generated at T0= 4.55,4.59,4.65,4.69and4.71in an effort to determine T c more accurately.Two methods were used.At smaller lattice sizes(L=12−27),finite-size scaling of extrema in the suceptibilityχ′,as well as the logarithimic derivative of the order parameter V1(see Ref.[3] for definitions),were made for both spin and chiral order parameters.Scaling made with the assumption of tricriticality(ν=1bility that the smaller lattices used in this simulation were not sufficiently large to accomo-date the true critical behavior,scaling of thermodynamic quatities with the functional form F1=a+bL x was considered in addition to the usual assumption F2=bL x.(Of course, only the form F1was used for the specific heat).Differences between the estimated critical exponents using these twofitting functions varied considerably.This is believed to be a reflection of the different relative strengths offinite-size effects depending on the thermody-namic quantity under consideration[20].In some cases,strong effects were also found if the smaller values of L were not included in thefit.In general,greaterfitting-procedure effects were found for the scaling at the lower tem-perature,T=4.673.Exponent estimates were generally larger if the form F1was used and increased(in most cases)if the smaller L data were excluded.For example,in the case of the specific heat C(where x=α/ν),exponent values1.3(3),1.7(5),and2.5(10)(where errors reflect only the robustness of thefit)were found using only data for L=18-33,21-33,and 24-33,respectively.The dependence of exponent estimates on the assumedfitting function, as well as excluded data,are presented in Table I forχ′(x=γ/ν),V1(x=1/ν),and the order parameter M(x=−β/ν).(Only results offitting the form F2to M are presented due to the large errors found if the form F1is assumed).The results of thesefits are very suggestive of afirst-order transition.Note that although no discontinuity is observed in M(T)at T c,the small exponent value is indicative of a very sharp rise near the transition, as expected if a jump in M is smoothed-out due to significantfinite-size effects.Confirmation thatfinite-size scaling at T=4.673indicates afirst-order transition is demonstrated by Figs.2-4where good asymptotic straight-linefits are found with the assumption that x=3for C,χ′and V1for both spin and chiral order.The data presented in this manner are convincing in view of the discussion in Ref.[20],and in particular,of the similar scaling found in II for the transition to the3-state Potts phase.Although it is known from rigorous symmetry arguments that the3-state Potts transition is indeedfirst order,this is revealed only at the larger lattice sizes in MC simulations and is indicative of a very small latent heat.The observation of only asymptotic volume dependence at aweakfirst order transition has been previously emphasized[20].Similar conclusions can be made regarding the present model.That the transition here is indeed only very weaklyfirst order,is also evident by the observation of a single peak in the energy histograms as well as our estimate for the energy cumulant(see I and II),U∗=0.6666631(3).In addition, the assumption of tricritical exponents yields scaling as in Figs.2-4with a noticable(but small)inferior quality based on goodness-of-fit(R2)tests.In contrast to these results,finite-size scaling at the higher temperature T=4.695yields exponents closer to those expected of tricritical behavior(and with diminished effects due to the smaller lattices),whereα/ν=1,β/ν=1Perhaps the recent theoretical work of Azaria et al.[11]is most relevant.Their conclusion that true critical behavior may be revealed with MC simulations only by using relativley large lattices is fully consistent with the present results and may eventually be proven relevant for the Heisenberg model.Conclusion regarding the critical behavior in the somewhat-quasi-one-dimensional (J /J⊥≃−5)compound CsCuCl3also appear to support the scenario of a very weak first order transition for frustrated XY systems[6].These specific-heat data indicate an unusually large exponentα≃0.35,suggestive of tricritical behavior,except very close to the transition wherefirst-order behavior is observed.A similar scenario has also been put forth based on the analysis of experimental data on several rare-earth helimagnets[21].In conclusion,thefinite-size scaling analysis presented here is thefirst evidence from MC simulations that the frustrated hexagonal antiferromagnet exhibits a weakfirst order phase transition to the paramagnetic state.This work serves to strengthen the conclusions of several older,and also the most recent,of4−ǫRG analyses as well as new studies based on the NLσmodel.In addition,a clearer picture is emerging(proximity of the3-state Potts phase)that explains the difficulty in treating this long-standing problem theoretically, experimentally and numerically.ACKNOWLEDGMENTSWe thank E.Sorensen for suggesting this work,U.Schotte for discussions on CsCuCl3, and the Service de l’Informatique for the partial use of10RISC6000Workstations.This work was supported by NSERC of Canada and FCAR du Qu´e bec.REFERENCES[1]H.Kawamura,Phys.Rev.B38,4916(1988);J.Phys.Soc.Jpn.61,1299(1992).[2]P.Azaria,B.Delamotte,and Th.Jolicoeur,Phys.Rev.Lett.64,3175(1990);P.Azaria,B.Delamotte,F.Delduc,and Th.Jolicoeur,Nucl.Phys.B408,485(1993).[3]See,e.g.,A.Mailhot,M.L.Plumer,and A.Caill´e,Phys.Rev.B50,6854(1994).[4]M.L.Plumer and A.Mailhot,Phys.Rev.B50,16113(1994).[5]M.L.Plumer,A.Mailhot,and A.Caill´e,Phys.Rev.B48,3840(1993);ibid49,15133(1994).[6]H.B.Weber,T.Werner,J.Wosnitza,H.v.L¨o hneysen,and U.Schotte,Phys.Rev.Lett.(submitted).[7]M.L.Plumer and A.Mailhot in Computer Simulation Studies in Condensed MatterPhysics 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and G.H.F.Brits,J.Phys.:Cond.Matt.7,9863(1995).TABLESTABLE I.Dependence of exponents x on the assumed critical temperature,fitting function (see text)and excluded data.Errors indicate only the robustness of thefit.T=4.673F1F2χ′ 2.9(1) 2.7(1) 2.8(1) 2.36(4) 2.38(4) 2.41(4) V1 2.3(1) 2.5(2) 2.7(3) 2.00(5) 2.02(6) 2.07(6) M-0.365(5)-0.364(8)-0.347(3)T=4.695χ′ 2.17(6) 2.3(1) 2.2(2) 2.12(2) 2.12(2) 2.13(2) V1 1.83(7) 1.9(1) 1.9(2) 1.78(1) 1.78(2) 1.79(2) M-0.48(1)-0.501(7)-0.51(1)FIGURESFIG.1.(a)Spin order-parameter cumulant crossing as a function of inverse temperature (β=1/T)for the lattice sizes indicated.(b)Corresponding results for chiral order.FIG.2.Finite-size scaling at T=4.673of the specific heat data for L=12−33.Data at L=12-21are excluded from thefit.Error bars are estimated from the standard deviation found in the MC runs.FIG.3.Finite-size scaling at T=4.673of the spin susceptibilityχ′as well as the logarithmic derivative of the order parameter V1(see text).Data at L=12-18are excluded form thefit.FIG.4.Thermodynamic functions associated with chiral order,as in Fig.3.11。