Ginzburg criterion for the chiral transition

This report is based on the work done together with J.B. Kogut and C,G. Str outhos. We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number N of fermions near the finite temperature phase tra nsition. Critical properties in such a system can be described by the mean field theory very close to the transition point. We show that the width of the window of non-trivial scaling is suppressed by a certain power of 1/N. Our Monte Carlo simulations confirm these analytical results. We discuss im plications for the chiral phase transition in QCD.