Can the chiral transition in QCD be described by a linear sigma-model in three dimensions?

Abstract

On a three-dimensional lattice, we simulate linear sigma-models of GL(n, C) matrices for n=1, 2, 3. Our results suggest that the phase structures which had been conjectured on the basis of renormalization-group studies are indeed correct: the transition is second order for n=1 and first order for n=2, 3. These first-order transitions terminate in second-order lines in the O(2 n 2)-symmetric limits of these models. In the presence of determinant terms, the n=2 transition ceases to be first order unless the coupling of this term is very small. By contrast, the n=3 transition remains first order even for large determinant couplings. These phase structures agree well with recent results on the chiral-symmetry restoration transitions in finite-temperature QCD with various quark flavors.