Using the monomer-dimer representation of strongly coupled U(N) lattice gauge
theories with staggered fermions, we study finite temperature chiral phase
transitions in (2+1) dimensions. A new cluster algorithm allows us to compute
monomer-monomer and dimer-dimer correlations at zero monomer density (chiral
limit) accurately on large lattices. This makes it possible to show
convincingly, for the first time, that these models undergo a finite
temperature phase transition which belongs to the Kosterlitz-Thouless
universality class. We find that this universality class is unaffected even in
the large N limit. This shows that the mean field analysis often used in this
limit breaks down in the critical region.Comment: 4 pages, 4 figure
We perform a detailed numerical investigation of the dynamics of broken
symmetry λϕ4 field theory in 1+1 dimensions using a
Schwinger-Dyson equation truncation scheme based on ignoring vertex
corrections. In an earlier paper, we called this the bare vertex approximation
(BVA). We assume the initial state is described by a Gaussian density matrix
peaked around some non-zero value of ,andcharacterizedbyasingleparticleBose−Einsteindistributionfunctionatagiventemperature.Wecomputetheevolutionofthesystemusingthreedifferentapproximations:Hartree,BVAandarelated2PI−1/Nexpansion,asafunctionofcouplingstrengthandinitialtemperature.IntheHartreeapproximation,thestaticphasediagramshowsthatthereisafirstorderphasetransitionforthissystem.Aswechangetheinitialstartingtemperatureofthesystem,wefindthattheBVArelaxestoanewfinaltemperatureandexhibitsasecondorderphasetransition.WefindthattheaveragefieldsthermalizeforarbitraryinitialconditionsintheBVA,unlikethebehaviorexhibitedbytheHartreeapproximation,andweillustratehow and dependontheinitialtemperatureandonthecouplingconstant.Wefindthatthe2PI−1/Nexpansiongivesdramaticallydifferentresultsfor.Comment: 28 pages, 21 figures; ver 2 -- additional comments on the nature of
the phase transition in 1+1 dimension