PHASE-TRANSITIONS AT FINITE-TEMPERATURE AND DIMENSIONAL REDUCTION FORFERMIONS AND BOSONS

In a recent letter we discussed the fact that large-N expansions and c omputer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Ne veu model is mean field theory. This was seen to be a counterexample t o the standard 'sigma model' scenario which predicts the 2D Ising mode l universality class. In this article we present more evidence, both t heoretical and numerical, that this result is correct. We develop a ph ysical picture for our results and discuss the width of the scaling re gion (Ginzburg criterion), 1/N corrections, and differences between th e dynamics of BCS superconductors and Gross-Neveu models. Lattices as large as 12 x 72(2) are simulated for both the N = 12 and N = 4 cases and the numerical evidence for mean field scaling is quite compelling. We point out that the amplitude ratio for the model's susceptibility is a particularly good observable for distinguishing between the dimen sional reduction and the mean field scenarios, because this universal quantity differs by almost a factor of 20 in the two cases. The simula tions are done close to the critical point in both the symmetric and b roken phases, and correlation lengths of order 10 are measured. The cr itical indices beta(mag) and delta also pick out mean field behavior. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the composite character of the mesons in the mod el. We point out that our results should be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics. We also s imulated the O(2) model on 8 x 16(3) lattices to establish that our me thods give the results of dimensional reduction in purely bosonic case s where its theoretical basis is firm. We also show that Z(2) Nambu-Jo na-Lasinio models simulated on 8 x 16(3) lattices give mean field rath er than three-dimensional Ising model indices.