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

Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance