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

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