Large-N_f chiral transition in the Yukawa model

Abstract

We investigate the finite-temperature behavior of the Yukawa model in which $N_f$ fermions are coupled with a scalar field $\varphi$ in the limit $N_f\to \infty$. Close to the chiral transition the model shows a crossover between mean-field behavior (observed for $N_f=\infty$) and Ising behavior (observed for any finite $N_f$). We show that this crossover is universal and related to that observed in the weakly-coupled ${\varphi }^4$ theory. It corresponds to the renormalization-group flow from the unstable Gaussian fixed point to the stable Ising fixed point. This equivalence allows us to use results obtained in field theory and in medium-range spin models to compute Yukawa correlation functions in the crossover regime.