Large-N_f chiral transition in the Yukawa model

TL;DR

This paper studies the finite-temperature chiral transition in the large-$N_f$ Yukawa model, revealing a universal crossover from mean-field to Ising behavior linked to renormalization-group flow, with implications for correlation functions.

Contribution

It demonstrates the universality of the crossover in the Yukawa model and connects it to well-understood field theory and spin model results, providing new insights into the transition behavior.

Findings

Crossover between mean-field and Ising behavior near the chiral transition.

Universality of the crossover related to RG flow from Gaussian to Ising fixed point.

Application of field theory and spin model results to Yukawa correlation functions.

Abstract

We investigate the finite-temperature behavior of the Yukawa model in which $N_{f}$ fermions are coupled with a scalar field $\phi$ 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 $\phi^4$ 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.