a r X i v :h e p -l a t /9612011v 1 14 D e c 1996
1
Finite -Temperature QCD on the Lattice
Akira Ukawa a
a
Institute of Physics,University of Tsukuba,Tsukuba,Ibaraki 305,Japan
Recent developments in ?nite-temperature studies of lattice QCD are reviewed.Topics include (i)tests of improved actions for the pure gauge system,(ii)scaling study of the two-?avor chiral transition and restoration of U A (1)symmetry with the Kogut-Susskind quark action,(iii)present understanding of the ?nite-temperature phase structure for the Wilson quark action.New results for ?nite-density QCD are brie?y discussed.
1.Introduction
Finite-temperature studies of lattice QCD have been pursued over a number of years.Quite clearly the pure gauge system is the best under-stood of the entire subject.The system has a well-established ?rst-order decon?nement transi-tion[1],and extensive and detailed results are al-ready available for a number of thermodynamic quantities[2].Nonetheless many new studies have been made for this system recently.The purpose is to examine to what extent cuto?e?ects in ther-modynamic quantities are reduced for improved actions as compared to the plaquette action which had been used almost exclusively in the past.Full QCD thermodynamics with the Kogut-Susskind quark action has also been investigated extensively in the past.A basic question for this system is the order of chiral phase transition for light quarks.For the system with two ?avors,?nite-size analyses carried out around 1989-1990indicated an absence of phase transition down to the quark mass m q /T ≈0.05[3],and a more re-cent study[4]attempted to ?nd direct evidence for the second-order nature of the transition,as sug-gested by the sigma model analysis in the contin-uum[5],through scaling analyses.Scaling studies have been continued this year to establish the uni-versality nature of the transition on a ?rm basis.Another issue discussed at the Symposium is the question of restoration of U A (1)symmetry at the chiral transition.Results have been presented for equation of state both without and with use of improved actions.
Studies of thermodynamics with the Wilson
quark action is much less developed compared to that for the Kogut-Susskind quark action.Past simulations found a number of unexpected fea-tures,which made even an understanding of the phase structure a non-trivial problem[6].Re-cently,however,considerable light has been shed on this problem through an analysis based on the view that the critical line of vanishing pion mass marks the point of a second-order phase transi-tion which spontaneously breaks parity and ?avor symmetry[7].Some new work with improved ac-tions,which was initiated a few years[8],has also been made this year.
In this article we review recent studies of ?nite-temperature lattice QCD.In Sec.2we summarize results for the pure gauge decon?nement tran-sition obtained with a variety of improved ac-tions.Results for the two-?avor chiral transition for the Kogut-Susskind quark action are discussed in Sec.3with the main part devoted to scaling analyses of the order of the transition.In Sec 4we describe recent progress on the phase struc-ture analysis for full QCD with the Wilson quark action.This year’s results for ?nite density are brie?y discussed in Sec 5.Our summary and con-clusions are presented in Sec.6.
2.Recent work on pure gauge system In Table 1we list recent studies of the pure gauge system using improved actions.Among ac-tions constructed through renormalization group,RG(1,2)[18]includes 1×2loop in addition to the plaquette.The action FP is an 8-parameter ap-proximation to the ?xed point action[9]contain-
2
Table1
Recent work on pure gauge system with improved actions.Argument forβc means spatial volume,μ(L)the torelon mass for spatial size L and N t the temporal lattice size.
RG-improved
S(1,2)tree[14]βc(4N t)3,4,5,6
[15]βc(∞),σ,?,p,σI4
S(1,2)tadpole[15]βc(∞),σ,?,p,σI4
S(2,2)tree[16,15]βc(∞),σ,?,p4 SLW tadpole[17]βc(2N t),μ(L)2,3,4
[13]βc(∞),μ(L)2,3
σ
A basic quantity for the pure gauge system is
√
the ratio T c/
3 aT c=0.25where values for six types of ac-
tions are available.Among those belonging to
the category of Symanzik improvement,we ob-
√
serve that T c/
σ≈0.64.If we take
√
T c/
σ(L)
Another quantity often used for testing im-
provement with simulations on small lattices
is the torelon massμ(L)extracted from the
Polyakov loop correlator on a lattice of spatial size
L.De?ningσ(L)=μ(L)/L we compile in Fig.2
results for the ratio T c/
4
ref.size m
q
5
up to 123,but stays constant within errors be-tween 123and 163both at m q =0.025and 0.0125?0.01(see Fig.11and 12in the second paper of ref.[27]).The saturation implies the ab-sence of a phase transition down to m q ≈0.01.Since this quark mass is quite small,correspond-ing to m π/m ρ≈0.2at the point of the transition βc ≈5.27,it was thought that the result is con-sistent with the transition being of second order at m q =0as suggested by the sigma model anal-ysis[5].
3.1.1.Scaling analysis of susceptibilities One can attempt to examine if the transition is of second order employing the method of scaling analysis.Let us de?ne the susceptibilities χm and χt,i (i =f,σ,τ)by
χm =V
(
qq 2 (3)χt,f =V [ qD 0q ? qD 0q ](4)χt,i
=
V [
qq P i ],i =σ,τ(5)
with V =L 3N t ,D 0the temporal component of the Dirac operator,and P σ,τthe spatial and tem-poral plaquette.For a given quark mass m q ,let g ?2c (m q )be the peak position of χm as a func-tion of the coupling constant g ?2,and let χmax m and χmax t,i
(i =f,σ,τ)be the peak height.For a second-order transition,these quantities are ex-pected to scale toward m q →0as
g ?2c (m q )=
g ?2c (0)+c g m z g
q
(6)χmax m =c m m ?z m q (7)χmax t,i
=
c t,i m ?z t,i
q
,i =f,σ,τ
(8)
Let us note that χt,i (i =f,σ,τ)are three parts of
the susceptibility χt =V [ qq ? ]with ?the energy density[4].The leading exponent is therefore given by z t =Max(z t,f ,z t,σ,z t,τ).
Natural values to expect for the exponents z g ,z m and z t at a ?nite lattice spacing are those of O (2)≈U (1)corresponding to the exact sym-metry group of the Kogut-Susskind action.How-ever,su?ciently close to the continuum limit where ?avor breaking e?ects are expected to dis-appear,they may take the values for O (4)≈SU (2)?SU (2)which is the group of chiral sym-metry for N f =2in the continuum.One should also remember that mean-?eld exponents control
the scaling behavior not too close to the transi-tion.A possibility of mean-?eld exponents arbi-trarily close to the critical point has also been discussed[30].
The initial scaling study was carried out by Karsch and Laermann[4]employing an 83×4lat-tice and m q =0.02,0.0375,https://www.doczj.com/doc/8711430139.html,pared to the O (4)values their results for exponents show a good agreement of z m ,a 50%larger value for z g and a value twice larger for z t .Comparison with O (2)and mean-?eld exponents is similar since they are not too di?erent from the O (4)values.This work had limitations in several respects:(i)the scaling formulae are valid for a spatial size large enough compared to the correlation length.At m q =0.02the pion correlation length equals ξπ≈3.Whether the spatial size of L =8em-ployed is su?ciently large has to be examined.(ii)The size of the scaling region in terms of quark mass is a priori not known.Hence the behavior for smaller quark masses should be ex-plored to check if the results are not a?ected by sub-leading and analytic terms in an expansion of susceptibilities in m q .(iii)In the original work the noisy estimator with a single noise vector was employed to estimate disconnected double quark loop contributions.This introduces contamina-tion from connected diagrams and local contact terms,which has to be removed.Other fac-tors such as step size of the hybrid R algorithm and stopping condition for the solver of Kogut-Susskind matrix could also a?ect the value of sus-ceptibilities.
For these reasons the Bielefeld group has con-tinued their study[28],and the JLQCD Collabo-ration[29]has started their own work last year.As one sees in Table 2run parameters of new simulations are chosen to examine the points (i)and (ii)above.In order to deal with (iii)Biele-feld group worked out the correction formula for the case of the single noise vector.They also employed the method of multiple noise vectors for some of the runs.JLQCD employed the method of wall source without gauge ?xing[31],and removed contamination by a correction for-mula.At present both groups have accumulated (5?10)×103trajectories of unit length with a small step size of δτ=(1?1/2)m q for each
6
z m 0.790.792/30.79(4) 1.05(8)0.93(9)
0.70(3) 1.01(11)1.02(7)
L =8to L =12?16is evident,with the val-ues for larger sizes sizably deviating from either O (4),O (2)or the mean-?eld predictions.For z g the deviation seems less apparent though full data are not yet available.
A puzzling nature of the values of exponents becomes clearer if we translate them into the more basic thermal and magnetic exponents y t and y h using the relations,z g =
y t
y h
,z t =
y t
y h
?1
(9)
with
d =3th
e space dimension.The values in Table 3are reasonably consistent with the rela-tion z g +z m =z t +1which follow from (9).We observe that z m ≈1.0(1)obtained for larger spa-tial lattices implies y h ≈3.0(3)to be compared with the O (4)value 2.49,while y h =d =3is ex-pected for a ?rst-order phase transition.For the thermal exponent we ?nd y t ≈2.4(3)i
f we take z t ≈0.8(1)or y t ≈2.7(3)for z t ≈0.9(1),which is substantially larger than the O (4)value of 1.34.One may think of various possibilities for the reason leadin
g to these values of exponents.(i)The most conventional would be that the in?uence of sub-leading and analytic terms is still sizable at the range of quark mass explored.(ii)Another possibility,suggested by the value y
h ≈d for L =12and 16,is that a disconti-
7 nuity?xed point with y h=d[33]controlling the
?rst-order
transition along the line m q=0in the
low-temperature phase is strongly in?uencing the scaling behavior.The transition is of second or-der in this case.Whether the deviation of y t from any of the expected values can be explained is not clear,however.(iii)The transition is of second or-der with the exponents close to but not equal to
d.This would mean a signi?cant departure from
the universality concepts,stepping even beyond the suggestion of mean-?eld exponents arbitrarily
close to the critical point[30].(iv)The transition is of?rst order.In this case,the value of quark
mass m q=m c q at which the?rst-order transition
terminates would have to be small or even vanish since the scaling formula is derived under the as-
sumption of a transition taking place at a single
point at m q=0.
Concerning the possibility(iv),results of
present data examined from?nite-size scaling point of view are as follows.As we already
pointed out,χm for a?xed value of m q stays
constant for L=12?16down to m q=0.02. Results for other susceptibilities exhibit a similar
behavior.Thus a phase transition does not exist
for m q≥0.02as concluded in the previous stud-ies[26,27].At m q=0.01the susceptibilities in-
crease by a factor3between L=8and16.Runs
for L=12are needed to see if the increase is con-sistent with a linear behavior in volume expected for a?rst-order transition.
We have to conclude that scaling analyses of
susceptibilities carried out so far do not allow a
de?nite conclusion.Much further work,possibly with a quark mass smaller than has been explored so far,is needed to elucidate the nature of the chiral transition for N f=2.
3.1.2.Scaling analysis of chiral order pa-
rameter
For a second-order transition the singular part
of the chiral order parameter is expected to scale as
qq generated on a123×6 lattice with m q=0.025and0.0125.Adding an analytic term of form m q(c0+c1/g2+c2/g4), the?t was found acceptable for O(4)and also for the mean-?eld scaling function.Extrapolat-ing to the limit m q=0,the results di?er signi?-cantly between the two cases,however(see Fig.2 of ref.[35]).
We note that the results of the present MILC analysis do not contradict those of susceptibili-ties:the quark mass used for this work corre-sponds to m q≈0.02?0.04on an83×4lattice, for which case the exponents found from suscepti-bilities are similar to the O(4)values.We further remind,however,that the exponents exhibit a sig-ni?cant size dependence.This means that stud-ies with larger lattice sizes and smaller m q are required to explore the nature of the two-?avor transition from scaling of the chiral order param-eter.
3.2.Restoration of U A(1)symmetry
For su?ciently high temperatures topologically non-trivial gauge con?gurations are suppressed, leading to restoration of U A(1)symmetry.To what extent U A(1)symmetry is restored close to the chiral transition is an interesting question. Three groups[35,37,28]examined the problem using the susceptibility de?ned by
χU
A
(1)
= d4x( π(x)· π(0) ? a0(x)· a0(0) )(10)
which should vanish at m q=0if U A(1)sym-metry is restored.In Fig.5we plot the m q de-pendence of this quantity obtained by the MILC Collaboration[35]and the Columbia group[37]. Both results are taken in the high temperature phase corresponding to T/T c≈1.2?1.3.While the data appear to extrapolate linearly to zero at m q=0(dotted lines)[37],it is more reason-
8
9
that the critical line should be de?ned by the van-
ishing of the quark mass m q at zero temperature, where m q is de?ned through chiral Ward iden-
tity[42,50,51].They reported that the crossing pointβct with this de?nition of the critical line
is located in the region of strong coupling on an
N t=4lattice,e.g.,βct≈3.9?4.0for N f=2. For the phase diagram based on this result see
ref.[6].
This phase diagram,however,has an unsatis-factory feature.It has been observed[48,49]that physical observables do not exhibit any singu-lar behavior across the critical line in the high temperature phase.This means that the region K≥K c(β),usually thought unphysical,is not distinct from the high temperature phase,be-ing analytically connected to it.Hence one can cross from the low-to the high-temperature phase through the part of the critical line belowβ=βct, which is not a line of?nite-temperature transi-tion.
Clearly the phase diagram above does not cap-
ture the full aspect of the phase structure.Re-cent investigations indicate that a more natural understanding of the phase structure is provided by a di?erent view on the critical line proposed by Aoki some time ago[7].In the following we review the phase structure based on this view. Let us note that a slightly di?erent phase struc-ture has been discussed in ref.[52].The phase structure for general values of N f up to N f=300 has also been examined recently[53].
4.2.Spontaneous breakdown of parity-
?avor symmetry and massless pion
In order to illustrate the basic idea,let us con-
sider an e?ective sigma model for lattice QCD with the Wilson quark action with N f=2.The e?ective lagrangian may be written as
L eff=(?μ π)2+(?μσ)2+a π2+bσ2+ (11)
where the coe?cients a and b di?er re?ecting ex-plicit breaking of chiral symmetry due to the Wil-son term.We know that the pion mass vanishes as a=m2π∝K c?K toward the critical line,while σstays massive,i.e.,b=m2σ>0at K≈K c.If K increases beyond K c,the coe?cient a becomes negative.Hence we expect the pion?eld to de-velop a vacuum expectation value π =0.The condensate spontaneously breaks parity and?a-vor symmetry.
Let us note that pion is not the Nambu-Goldstone boson of spontaneously broken chiral symmetry in this view.Instead it represents the massless mode of a parity-?avor breaking second-order phase transition which takes place at K=K c.We expect it to become the Nambu-Goldstone boson of chiral symmetry in the contin-uum limit,however,as chiral symmetry breaking e?ects disappear in this limit.
The idea above has been explicitly tested for the two-dimensional Gross-Neveu model formu-lated with the Wilson action[7].An analytic so-lution in the large N limit shows spontaneous breakdown of parity for K≥K c(β).Another important result of the solution is that the criti-cal line forms three spikes,which reach the weak-coupling limit g=0at1/2K=+2,0,?2.This structure arises from the fact that the doublers at the conventional continuum limit(g,1/2K)= (0,2)become physical massless modes at1/2K= 0and?2.
A close similarity of the Gross-Neveu model and QCD regarding the asymptotic freedom and chiral symmetry aspects leads one to expect a similar phase structure for the case of QCD ex-cept that the critical line will form?ve spikes reaching the continuum limit because of di?er-ence in dimensions[7].Evidence supporting such
a phase structure is summarized in ref.[54].
4.3.Finite-temperature phase structure For a?nite temporal lattice size N t correspond-ing to a?nite temperature,the above considera-tion can be naturally extend by de?ning the crit-ical line as the line of vanishing pion screening mass determined from the pion propagator for large spatial separations.
In Fig.6the critical line for the two-dimensional Gross-Neveu model calculated in the large N limit is plotted for N t=∞,16,8,4,2 starting from the outermost curve and moving to-ward inside.The result shows that the location of the critical line as de?ned above depends on N t.Another important point is that the spikes formed by the critical line moves away from the
10
1.5 1.00.50
g
2
1
-1
-2
1/2K Figure 6.Critical line in (g,1/2K )plane for the two-dimensional Gross-Neveu model for the tem-poral size N t =∞,16,8,4,2(from outside to in-side)[55].
weak-coupling limit as N t decreases.
Simulations to examine if lattice QCD has a similar structure of the critical line at ?nite temperatures have been made recently for the case of N f =2[55]and 4[56]on an 83×4lat-tice.The results are summarized as follows:(i)For both systems the conventional critical line turns back toward strong coupling forming a cusp,whose tip is located at β≈4.0for N f =2and β≈1.8for N f = 4.The cusp repre-sents one of ?ve cusps expected for lattice QCD.(ii)Parity and ?avor symmetry are spontaneously broken inside the cusp.Simulations have been made for the N f =2system with an exter-nal ?eld term δS W =2KH n
ψγ5τ3ψ =0of the parity-?avor order parameter and vanishing of π±mass
lim H →0m π±=0expected inside the cusp[56].Concerning the relation between the thermal line and the critical line,we recall that the pion mass vanishes all along the critical line.This suggests that the region close to the critical line is in the cold phase even after the critical line turns back toward strong coupling,and hence the thermal line cannot cross the critical line.Since numerical estimates show that the thermal line comes close to the turning point of the cusp,the natural possibility is that the thermal line runs past the tip of the cusp and continues toward larger values of K .Results of measurement of thermodynamic quantities provide support of
this
0.15
0.20
0.25
0.30
K
11
Indeed strong?rst-order signals have been ob-served for the case of N f=3[48]and4[56]away
from the critical line,as shown by solid squares in Fig.7,in contrast to a crossover behavior rep-
resented by open squares seen for N f=2.How-ever,the?rst-order transition for N f=4weak-ens closer to the critical line,apparently turning
into a smooth crossover before reaching the region around the cusp of the critical line as indicated by open rectangles[56].While parallel data are
not yet available for N f=3,results of the QCD-PAX Collaboration[48]also appears to indicate a
weakening of the?rst-order transition.
A possible reason for this unexpected behav-ior is that breaking of chiral symmetry due to
the Wilson term,which becomes stronger asβdecreases along the thermal line,smoothens the ?rst-order transition.Another possibility is that
the?rst-order transition for N f=3and4ob-served so far is a lattice artifact sharing its origin
with the sharpening of the crossover atβ≈5.0 found by the MILC Collaboration for N f=2[49]. Some support for this interpretation is given by
a recent study of the QCDPAX Collaboration for the N f=3system with an improved gauge ac-tion[57].So far they have not found clear?rst-
order signals in the region where the plaquette action shows a clear?rst-order behavior.
In either case,if chiral transition in the con-
tinuum is indeed of?rst order for N f=3and 4,it will emerge only when the cusp moves su?-
ciently toward weak-coupling with an increase of the temporal size N t.
4.5.Continuum limit
We expect the cusp of the?nite-temperature critical line to grow toward weak coupling as N t
increases.In the limit N t=∞it should con-verge to the zero-temperature critical line which reachesβ=∞.Since the thermal line is located
on the weak-coupling side of the cusp for a?nite N t,it will be pinched by the tip of the cusp at
(β,K)=(∞,1/8)as N t→∞.We expect chiral phase transition in the continuum to emerge in this limit.In order to extract continuum proper-
ties of the chiral transition,we then need a sys-tematic study of thermodynamic quantities in the neighborhood of the thermal line when it runs close to the tip of the cusp as a function of N t. Simulations,however,indicate that the cusp moves only very slowly as N t increases.For the N f=2case,current estimates of the position of the tip of the cusp isβ≈4.0for N t=4[55], 4.0?4.2for N t=6[48],4.2?4.3for N t=8[56] and4.5?5.0even for N t=18[48].A recent work also reports an absence of parity-broken phase aboveβ=5.0on symmetric lattices up to the size104[60].For N f=4the values are even lower:β≈1.80for N t=4and2.2?2.3for N t=8[56].These estimates indicate that a very large temporal size will be needed for the cusp to move into the scaling region(e.g.,β≥5.5for N f=2)as long as one employs the Wilson quark action together with the plaquette action for the gauge part.
We emphasize that this result has an impor-tant implication also for spectrum calculations at zero temperature.Since the location of the cusp is determined by the smaller of the spatial and temporal size,the critical line will be shifted or may even be absent unless lattice size is taken su?ciently large.Therefore hadron masses cal-culated on a lattice of small spatial size and ex-trapolated toward the position of the critical line might involve signi?cant systematic uncertainties.
4.6.Studies with improved actions
The problems discussed above indicate the presence of sizable cuto?e?ects when the Wil-son quark action is used in conjunction with the plaquette action.A way to alleviate this problem is to employ improved actions.This approach has been pursued by the QCDPAX Collabora-tion[8,57],replacing the plaquette action with an improved gauge action RG(1,2)[18].This year the MILC Collaboration reported simulations with the action SLW tadpole for the gauge part and the tadpole-improved clover action for the quark part[58].Results with the tree-level clover ac-tion keeping the plaquette action are also avail-able[59].Thus there are data for four types of action combinations,unimproved and improved both for the gauge and quark actions,to make a comparative study of improvement.
An indication from such a comparison is that improving the gauge action substantially removes
12
cuto?e?ects.An in?ection of the critical line seen for the plaquette action atβ≈4?5becomes absent with improvement of the gauge action[8], while it still seems to remains if only the Wilson quark action is replaced by the clover action[59]. Also an intermediate sharpening of the thermal transition seen for the plaquette action atβ≈5.0[49]is not observed for improved actions[8,58]. Another point to note is that the lattice spacing at the coupling constant where the thermal line approaches the critical line has a similar value mρa≈1on an N t=4lattice for all of the four action combinations.This means that studies of physical quantities are needed to assess reduction of cuto?e?ects with improved actions.Interest-ing results have already been obtained for scaling of the chiral order parameter[8,61],and work with the critical temperature is being pursued[8,58].
5.Results in?nite density studies
It has long been known that the quenched ap-proximation breaks down for a non-zero quark chemical potentialμin that a transition takes place atμ≈mπ/2rather than atμ≈m N/3[62, 63].While the importance of the phase of the quark determinant has been made clear, the mechanism how the quenched approximation breaks has not been fully explained.
Recently Stephanov[64],employing a random matrix model of the quark determinant[65]and a replica formulation of quenched approximation, traced back the failure of the quenched approxi-mation to the non-uniformity of the limit of the replica number n→0forμ=0andμ>0.He has also shown that the quenched approximation is valid for the theory in which a quarkχin the conjugate representation is added to each quark q.Formation of a condensate
χq≈mπin such a theory explains the occurance of transition at μ≈mπ/2.
Barbour and collaborators reported new results in full QCD simulations[66].With the method of fugacity expansion[67]runs were carried out for four?avors of quarks on64and84lattices at β=5.1with the Kogut-Susskind quark action. They found an onset of non-zero baryon number at a small value ofμ,e.g.,μc≈0.1at m q=0.01. For comparison the MT c Collaboration reported m N=1.10(6)and mπ=0.290(6)at a slightly larger coupling ofβ=5.15at m q=0.01[68].
It is not yet clear if these results mean that an early onset of transitionμc≈mπ/2also holds for full QCD or re?ect computational problems of the method employed for the simulation.
6.Conclusions
Much work has been made in?nite tempera-ture studies of lattice QCD encompassing a num-ber of subjects during the last year.
Tests of improved actions made for the pure gauge system indicate a possibility that accurate results for thermodynamics in the continuum may be obtained with simulations carried out with a moderately large temporal size.
In full QCD studies much progress has been made in understanding the phase structure for the Wilson quark action.On the other hand, new problems have also been encountered,mak-ing it necessary to reexamine conclusions reached in previous studies.These are the unexpected val-ues of exponents for N f=2found in scaling stud-ies of susceptibilities with the Kogut-Susskind quark action,and the?avor dependence of or-der of chiral transition with the Wilson quark ac-tion.Elucidating these problems is important for reaching an understanding of the nature of chiral phase transition,which is consistent between the Kogut-Susskind and Wilson quark actions. Some progress has been made in QCD at?nite density.A puzzling result reported from the lat-est simulation shows,however,that we are still far from understanding this di?cult subject.
In closing we point out that most work in full QCD during the past several years have concen-trated on the case of N f degenerate quarks,espe-cially for N f=2.While a variety of basic prob-lems we have encountered for this case has to be clari?ed with further work,we should also recall that nature corresponds to the case of N f=2+1 with a heavier strange quark.A delicate change of phase that might possibly result from its pres-ence,as suggested in the continuum sigma model analysis[5],makes it important to enlarge previ-
13
ous studies[27,69,48]into a systematic e?ort in this direction.
Acknowledgements
I would like to thank S.Aoki, F.Beinlich, T.Blum,W.Bock,G.Boyd,M.Creutz,N. Christ,T.DeGrand,C.DeTar,M.Fukugita,Y. Iwasaki,K.Kanaya,T.Kaneko,F.Karsch,E. Laermann,P.Mackenzie,M.Okawa,D.Tous-saint,M.Wingate and Y.Yoshi′e for communicat-ing their results and for discussions.I would also like to thank S.Aoki,M.Fukugita,Y.Iwasaki, K.Kanaya and M.Okawa for comments on the manuscript.This work is supported in part by the Grant-in-Aid of the Ministry of Education, Science and Culture(Nos.04NP0801,08640349). REFERENCES
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QCD改善项目管理制度代号 1 主题容与适用围 1.1 本制度规定了QCD改善项目管理的定义、层级分类、组织结构、管理流程、改善流程、评价与激励。 1.2 本制度适用于车桥公司QCD改善项目管理。 2 定义 对于一个异常的KPI指标或现存的问题点，研究其改善的可能性和效果，提出具体的改善方案并实施，以PDCA循环为管理思路，进行过程控制，以确保KPI指标的达成或现状改善的管理过程。 3 层级与分类 3.1 QCD改善项目层级：公司级改善项目、工厂(部)级改善项目（以下简称工厂级）、车间（科室）级改善项目（含总部科室，以下简称车间级）、班组、员工个人级改善项目（以下简称班组级）。 3.2 QCD改善项目分类: QCD改善课题分质量（Q）、成本（C）、交货期（D）、安全（S）、管理（M）等五个方面。 4组织结构 本管理制度规定了公司级、工厂级改善项目的组织结构及职责分工，依据“全面展开全员参与规管理提升水平”的工作指导思想，公司各部门应对车间级、班组级改善项目应成立相应的组织，明确职责分工，开展改善项目管理工作。 4. 1 公司领导对关系到公司战略、发展、重大课题进行审议并决策，公司级改善项目必须经过公司领导讨论通过方可有效。工厂级QCD改善项目必须经过工厂领导讨论通过后方可有效。 4.2 公司级、工厂级改善项目以多功能小组（项目小组）形式开展改善工作，项目负责人对本改善项目的计划、实施、进度、目标达成负全责，可以跨越部门、行政权限，调动资源确保实施进度、目标顺利达成，并对项目成员及涉及部门工作开展情况实施评价、提出考核激励意见。
4.3 公司各部门是涉及QCD改善项目实施的主体单元，对所承接的改善项目容的进度、目标达成负责，接受项目小组的评价及考核激励意见。 4.4 生产规划部QCD室是公司QCD改善项目的归口管理部门：负责组织公司级、工厂级改善项目的审议，确定公司级、工厂级QCD改善项目节点评价工作；组织公司级、工厂级改善项目总体验收；负责组织对QCD改善方法进行培训、指导，执行上级QCD管理部门的工作指导和安排。 4.5 质量部是公司质量改善项目的归口管理部门，负责公司质量改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.6 研发部是公司技术改善项目的归口管理部门，负责公司技术改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.7 生产规划部是公司生产管理、安全、环境、装备技术、装备管理改善项目的归口管理部门，负责公司生产管理、安全、环境、装备技术、装备管理改善项目的审议、确定及组织对公司级、工厂级QCD改善项目节点验收、评价工作。 4.8 财务信息部是公司成本改善项目的归口管理部门，负责公司成本改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.9 综合管理部是公司管理改善项目的归口管理部门，负责组织公司管理改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.10 党群工作部是群众性创新（含小改善）项目的归口管理部门，负责组织群众性创新项目的部门验收、评价及成果发表等工作。 5 管理流程 5.1 改善项目来源 ①公司根据战略发展需要提出公司级重点改善课题； ②上级部门指令性改善课题； ③各级部门根据活动计划异常管理项目或异常指标提出有针对性的改善课题； ④工厂根据工厂发展需要由厂务会提出工厂级重点改善课题； ⑤各级部门以与时俱进的精神提出自主改善课题； ⑥根据现场管理的推进需要提出改善课题；
QCD改善项目管理制度代号 1 主题内容与适用范围 1.1 本制度规定了QCD改善项目管理的定义、层级分类、组织结构、管理流程、改善流程、评价与激励。 1.2 本制度适用于车桥公司QCD改善项目管理。 2 定义 对于一个异常的KPI指标或现存的问题点，研究其改善的可能性和效果，提出具体的改善方案并实施，以PDCA循环为管理思路，进行过程控制，以确保KPI指标的达成或现状改善的管理过程。 3 层级与分类 3.1 QCD改善项目层级：公司级改善项目、工厂(部)级改善项目（以下简称工厂级）、车间（科室）级改善项目（含总部科室，以下简称车间级）、班组、员工个人级改善项目（以下简称班组级）。 3.2 QCD改善项目分类: QCD改善课题分质量（Q）、成本（C）、交货期（D）、安全（S）、管理（M）等五个方面。 4组织结构 本管理制度规定了公司级、工厂级改善项目的组织结构及职责分工，依据“全面展开全员参与规范管理提升水平”的工作指导思想，公司各部门应对车间级、班组级改善项目应成立相应的组织，明确职责分工，开展改善项目管理工作。 4. 1 公司领导对关系到公司战略、发展、重大课题进行审议并决策，公司级改善项目必须经过公司领导讨论通过方可有效。工厂级QCD改善项目必须经过工厂领导讨论通过后方可有效。 4.2 公司级、工厂级改善项目以多功能小组（项目小组）形式开展改善工作，项目负责人对本改善项目的计划、实施、进度、目标达成负全责，可以跨越部门、行政权限，调动资源确保实施进度、目标顺利达成，并对项目成员及涉及部门工作开展情况实施评价、提出考核激励意见。
4.3 公司各部门是涉及QCD改善项目实施的主体单元，对所承接的改善项目内容的进度、目标达成负责，接受项目小组的评价及考核激励意见。 4.4 生产规划部QCD室是公司QCD改善项目的归口管理部门：负责组织公司级、工厂级改善项目的审议，确定公司级、工厂级QCD改善项目节点评价工作；组织公司级、工厂级改善项目总体验收；负责组织对QCD改善方法进行培训、指导，执行上级QCD管理部门的工作指导和安排。 4.5 质量部是公司质量改善项目的归口管理部门，负责公司质量改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.6 研发部是公司技术改善项目的归口管理部门，负责公司技术改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.7 生产规划部是公司生产管理、安全、环境、装备技术、装备管理改善项目的归口管理部门，负责公司生产管理、安全、环境、装备技术、装备管理改善项目的审议、确定及组织对公司级、工厂级QCD改善项目节点验收、评价工作。 4.8 财务信息部是公司成本改善项目的归口管理部门，负责公司成本改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.9 综合管理部是公司管理改善项目的归口管理部门，负责组织公司管理改善项目的审议、确定及组织公司级、工厂级QCD改善项目节点验收、评价工作。 4.10 党群工作部是群众性创新（含小改善）项目的归口管理部门，负责组织群众性创新项目的部门验收、评价及成果发表等工作。 5 管理流程 5.1 改善项目来源 ①公司根据战略发展需要提出公司级重点改善课题； ②上级部门指令性改善课题； ③各级部门根据活动计划异常管理项目或异常指标提出有针对性的改善课题； ④工厂根据工厂发展需要由厂务会提出工厂级重点改善课题； ⑤各级部门以与时俱进的精神提出自主改善课题； ⑥根据现场管理的推进需要提出改善课题；
qcd改善先进汇报 qcd改善先进汇报 QCD管理 “QCD”管理是指质量（Quality）、成本（Cost）与交货期（delivery）的管理，要求以优异的质量、最低的成本、最快的速度向用户提供最好的产品。 Quality,Cost,andDelivery，常简写为QCD,是品质、成本、与交付在精简生产方式（leanmanufacturing）中用以衡量商业活动并用以计算关键绩效指标（KeyPerformanceIndicators,KPI）。QCD的分析通常可以持续的改进商业活动的运作。QCD在很多不同类型的产业中都可适用，例如供应链产业、或是工程产业。QCD在专案管理领域中也常被拿来作为评估专案进展与决策的参考之一。 分析QCD的好处 QCD提供了一个很直觉的方法来衡量并评估简易与复杂的商业程序中，哪一种较为合适。它也提供了一个商业的比较基准。当品质、成本、与交付时程的其中之一必须改变时，借由QCD的分析可以有助于决策者做出决策。此外，在日常的商业运作当中，定期且事实的借由QCD的分析，也可追踪这三个要素是否均衡的被兼顾，解此可确保商业运作的顺利。QCD于专案管理上的应用 QCD有时也应用在专案管理上，不过一般而言，在专案管理上较常专注于专案范畴、成本、与时间（Scope,Cost,Time）。这三个变量为专案管理过程当中的三个重要变量，并且彼此相互牵连。
专案的范畴：在专案开始进行时便应已明确的定义，而会被拿来衡量的是品质。一般而言，当投注相当的时间与成本于专案的进行时，相对的会有一定的品质产出，然而，当时间与成本受限时，品质也许就会被牺牲。 专案的成本：成本虽然在专案开始前会大致估算，然而，随着专案的进行，相当多的变异都会影响额外成本的资出，诸如难度的低估、需要更多的人力或时间等。当专案进度落后，而交期又不可延展，并且品质也不可妥协时，通常会考虑增加生产力以加速进度，增加的生产力对应的就是成本的增加。 专案的时间：时间反应到专案最后的交付，当专案的工作被细部分解以排定各项工作所需时间后，专案便会依照拟定的进度进行。然而，彼此相互牵连的工作，意味着前期工作进度的落后将会影响最终是否可以准时交付成品。时间一般而言不算是一种成本，因为真正的成本是实际多少资源的投入，因此时间也许是可以妥协的，当客户希望所交付的成品必须维持一定品质，并且也不愿意增加经费以加快生产速度，而专案团队也无法借由自行吸收成本增加生产力，这时便可能针对可否延迟交期来进行讨论。 由此可见，事实上专案管理中的三个主要变量：范畴、成本、与时间，事实上与精简生产方式所谈的：品质、成本、与交付相当，也都是两两相依，相互影响。 能善用品质、成本、与交付，或是范畴、成本、与时间这两两相依的三个要素，便可改进管理的成效，确保生产的一贯品质与预期的交付。
QCD管理 “QCD”管理是指质量（Quality）、成本（Cost）与交货期（delivery）的管理，要求以优异的质量、最低的成本、最快的速度向用户提供最好的产品。 Quality, Cost, and Delivery，常简写为QCD,是品质、成本、与交付在精简生产方式（lean manufacturing）中用以衡量商业活动并用以计算关键绩效指标（Key Performance Indicators, KPI）。QCD 的分析通常可以持续的改进商业活动的运作。 QCD 在很多不同类型的产业中都可适用，例如供应链产业、或是工程产业。QCD 在专案管理领域中也常被拿来作为评估专案进展与决策的参考之一。 分析QCD 的好处 QCD 提供了一个很直觉的方法来衡量并评估简易与复杂的商业程序中，哪一种较为合适。它也提供了一个商业的比较基准。当品质、成本、与交付时程的其中之一必须改变时，借由QCD 的分析可以有助于决策者做出决策。此外，在日常的商业运作当中，定期且事实的借由QCD 的分析，也可追踪这三个要素是否均衡的被兼顾，解此可确保商业运作的顺利。 QCD 于专案管理上的应用 QCD 有时也应用在专案管理上，不过一般而言，在专案管理上较常专注于专案范畴、成本、与时间（Scope, Cost, Time）。这三个变量为专案管理过程当中的三个重要变量，并且彼此相互牵连。
专案的范畴：在专案开始进行时便应已明确的定义，而会被拿来衡量的是'品质。一般而言，当投注相当的时间与成本于专案的进行时，相对的会有一定的品质产出，然而，当时间与成本受限时，品质也许就会被牺牲。 专案的成本：成本虽然在专案开始前会大致估算，然而，随着专案的进行，相当多的变异都会影响额外成本的资出，诸如难度的低估、需要更多的人力或时间等。当专案进度落后，而交期又不可延展，并且品质也不可妥协时，通常会考虑增加生产力以加速进度，增加的生产力对应的就是成本的增加。 专案的时间：时间反应到专案最后的交付，当专案的工作被细部分解以排定各项工作所需时间后，专案便会依照拟定的进度进行。然而，彼此相互牵连的工作，意味着前期工作进度的落后将会影响最终是否可以准时交付成品。时间一般而言不算是一种成本，因为真正的成本是实际多少资源的投入，因此时间也许是可以妥协的，当客户希望所交付的成品必须维持一定品质，并且也不愿意增加经费以加快生产速度，而专案团队也无法借由自行吸收成本增加生产力，这时便可能针对可否延迟交期来进行讨论。 由此可见，事实上专案管理中的三个主要变量：范畴、成本、与时间，事实上与精简生产方式所谈的：品质、成本、与交付相当，也都是两两相依，相互影响。 能善用品质、成本、与交付，或是范畴、成本、与时间这两两相依的三个要素，便可改进管理的成效，确保生产的一贯品质与预期的交付。
QCD改善基层员工培训用题含答案（一） 1、我们应有的改善思想有哪些？ 答：A、抛开固有的观念。 B、马上就做，不讲理由。 C、不以金钱投入为借口，以智慧取胜。 D、找出【真因】，问五次【为什么】。 E、总想着现在还很差，改善无止境。 2、5S分别是什么？如何理解？ 答：5S:整理、整顿、清扫、清洁、素养 整理：将有用的和没用的分开，只对有用的进行管理，把没用的进行隔离或处理掉； 整顿：定位、定品、定量，以便减少寻找的时间，方便作业； 清扫：保持现场的清洁，确保现场、装备和零件的整洁； 清洁：对上述三个步骤成果标准化，以便维持和改善提升； 素养：使员工养成遵守标准的良好习惯，并不断地改善和提高。 3、什么是标准作业？ 答：能够确保安全、质量最好、生产效率最高的最佳的作业方法。 4、标准作业的四要素是什么？ 答：作业顺序、作业量（目标时间）、标准库存、作业要点。 5、什么是标准库存？ 答：指作业按照规定的要求能够连续顺畅生产所需的最低的库存量。 6、目标时间是什么含义？ 答：熟练作业者（L水平）在进行标准作业时所需要的时间。 7、简述目标时间的测量方法？ 答：A、确定作业者（能够正常进行标准作业）； B、在生产状态正常时进行测量； C、决定作业开始点； D、按照作业顺序，测定每一个步骤的时间，并记录汇总。 8、标准作业书有哪些种类？ 答：分解版、顺序版、编成版、组合版、流程版。 9、装配和机加常用的标准作业书分别是什么版本？ 答：装配常用的标准作业书是编成版； 机加常用的标准作业书是组合版。 10、作业重点是指什么？如何选取？ 答：作业重点是指在实施主要步骤中最重要的地方，如果不遵守，则会在质量、安全及可操作性上受到影响。 选取方法：A、从作业分解中选取，并在作业分解的重点地方画下划线； B、在补充主要步骤动作的要点、方法等中选取主要部分； C、如果一个主要步骤中有三个以上的重点，需要重新评估主要步骤的选 取是否合理； D、表达应该具体易懂。 11、什么是主体作业、附随作业、定型作业和非定型作业？ 答：主体作业：产生附加价值的作业，如：零部件装配、工具拿放等；