Critical region of the finite temperature chiral transition

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.