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

Abstract

We study the critical behavior of the three-dimensional Gross-Neveu (GN) model with ${N}_{f}$ four-component 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 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, which 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 nonperturbative realization of the GN quantum field theory, even though the lattice interactions explicitly break the flavor $\mathrm{U}({N}_{f})\ensuremath{\bigotimes}\mathrm{U}({N}_{f})$ symmetry of the GN field theory, which is only recovered in the critical limit.