Magnetic catalysis in the (2+1)-dimensional Gross-Neveu model

We study the Gross-Neveu model in $2+1$ dimensions in an external magnetic field $B$. We first summarize known mean-field results, obtained in the limit of large flavor number $N_\mathrm{f}$, before presenting lattice results using the overlap discretization to study one reducible fermion flavor, $N_\mathrm{f}=1$. Our findings indicate that the magnetic catalysis phenomenon, i.e., an increase of the chiral condensate with the magnetic field, persists beyond the mean-field limit for temperatures below the chiral phase transition and that the critical temperature grows with increasing magnetic field. This is in contrast to the situation in QCD, where the broken phase shrinks with increasing $B$ while the condensate exhibits a non-monotonic $B$-dependence close to the chiral crossover, and we comment on this discrepancy. We do not find any trace of inhomogeneous phases induced by the magnetic field.