We study a Yukawa theory with spontaneous chiral symmetry breaking and with a large number N of fermions near the finite temperature phase transition. 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 region where non-trivial critical behavior sets in is suppressed by a certain power of $1/N.$ Our Monte Carlo simulations confirm these analytical results. We discuss implications for the chiral phase transition in QCD.
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Kogut et al. (1998) studied this question.
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