Large-Nf chiral transition in the Yukawa model

We investigate the finite-temperature behavior of the Yukawa model in which Nf fermions are coupled with a scalar field ϕ in the limit Nf→∞. Close to the chiral transition the model shows a crossover between mean-field behavior (observed for Nf=∞) and Ising behavior (observed for any finite Nf). We show that this crossover is universal and related to that observed in the weakly-coupled ϕ4 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.