A FINITE-SIZED SCALING STUDY IN 3-DIMENSIONAL SU(N) X SU(N) AND U(N) X U(N) HEISENBERG MODELS AND FINITE-TEMPERATURE QCD

The chiral phase transition at finite temperature is simulated in a three-dimensional non-linear sigma model. Using both U(n) x U(n) and SU(n) x SU(n) flavor symmetries, the order of the chiral phase transition for n = 2 and n = 3 is numerically determined using lattice techniques. The SU(2) flavor symmetry is found to be second order while SU(3), U(2) and U(3) show first-order behavior. It is found that the strength of the first-order transition for U(2) and SU(3) is influenced by the long-wavelength modes on the lattice, with clear indications of a first-order transition only becoming apparent at large lattice sizes. A summary of these results for the chiral transition at finite temperature with the different flavor symmetries is presented, and some implications of the chiral symmetry restoration for SU(N) and U(N) flavor symmetries are discussed.