Chiral critical behavior of 3D lattice fermionic models with quartic interactions

TL;DR

This study investigates the critical behavior of 3D lattice Gross-Neveu models with multiple fermion flavors, using Monte Carlo simulations to estimate critical exponents and confirm the models' nonperturbative realization of continuum quantum field theory.

Contribution

It provides the first nonperturbative numerical analysis of 3D lattice Gross-Neveu models with staggered fermions, validating their critical behavior against large-N predictions.

Findings

Critical exponents agree with large-N continuum predictions

Lattice models recover flavor symmetry at criticality

Monte Carlo simulations confirm nonperturbative realization of GN theory

Abstract

We study the critical behavior of the three-dimensional (3D) Gross-Neveu (GN) model with $N_f$ Dirac fermionic flavors and quartic interactions, at the chiral ${\mathbb Z}_2$ transition in the massless ${\mathbb Z}_2$-symmetric limit. For this purpose, we consider a lattice GN model with staggered Kogut-Susskind fermions and a scalar field coupled to the scalar bilinear fermionic operator, which effectively realizes the attractive four-fermion interaction. We perform Monte Carlo (MC) simulations for $N_f=4,8,12,16$. By means of finite-size scaling analyses of the numerical data, we obtain estimates of the critical exponents that are compared with the large-$N_f$ predictions obtained using the continuum GN field theory. We observe a substantial agreement. This confirms that lattice GN models with staggered fermions provide a nonpertubative realization of the GN quantum field theory, even though the lattice interactions explicitly break the flavor ${\rm U}(N_f)\otimes {\rm U}(N_f)$ symmetry of the GN field theory, which is only recovered in the critical limit.