Lattice Gross-Neveu model with domain-wall fermions

We investigate the two-dimensional lattice Gross-Neveu model, using the domain-wall fermion formulation, as a toy model of lattice QCD. We study features of the phase diagram related to the mechanism of chiral symmetry restoration, and find that the parity-broken phase (Aoki phase) exists for finite extent in the extra dimension ($N_s$). We also find that O(a) scaling violation terms vanishes in the limit of $N_s\to\infty$.