  In this work, the phase diagram of the $2+1$-dimensional Gross-Neveu model is
investigated with baryon chemical potential as well as chiral chemical
potential in the mean-field approximation. We study the theory using two
lattice discretizations, which are both based on naive fermions. An
inhomogeneous chiral phase is observed only for one of the two discretizations.
Our results suggest that this phase disappears in the continuum limit.
