On the equivalence between 2D Yukawa and Gross-Neveu models

TL;DR

This study numerically compares the 2D Yukawa and Gross-Neveu models, revealing their equivalence in universality class across a broad parameter range, with potential new classes at crossover points.

Contribution

It demonstrates the universality between 2D Yukawa and Gross-Neveu models beyond weak coupling using lattice simulations and mean field analysis.

Findings

Yukawa and Gross-Neveu models share the same universality class.

Universality extends beyond weak coupling to a broad parameter range.

Possible new universality classes at the crossover to spin models.

Abstract

We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed using the mean field method. It is found to agree with that of the Gross-Neveu model with the same symmetry and $N_F$. The results suggest that the 2D Yukawa models belong to the universality class of the Gross-Neveu models not only at weak scalar field self-coupling but also for a broad range of the bare parameters which is not accessible to the $1/N_F$ expansion. New universality classes might arise at the crossover to the spin model universality class, however.