Two-dimensional lattice Gross-Neveu model with domain-wall fermions

Abstract

We investigate the two-dimensional lattice Gross-Neveu model in the large flavor number limit using the domain-wall fermion formulation as a toy model of lattice QCD. We study the nonperturbative behavior of the restoration of the chiral symmetry of the domain-wall fermions as the extent of the extra dimension ${(N}_{s})$ is increased to infinity. We find the parity broken phase (Aoki phase) for finite ${N}_{s},$ and study the phase diagram, which is related to the mechanism of chiral restoration in the ${N}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. The continuum limit is taken and the $O(a)$ scaling violation of observables vanishes in the ${N}_{s}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. We also examine the systematic dependencies of observables to the parameters.