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 f , before presenting lattice results using the overlap discretization to study one reducible fermion flavor, N 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. If you use this software, please cite the corresponding paper: https://doi.org/10.48550/arXiv.2302.05279 (or better the not-yet-existing published version)

This work has been funded by the Deutsche Forschungs- gemeinschaft (DFG) under Grant No. 406116891 within the Research Training Group RTG 2522/1. The simula- tions were performed on resources of the Friedrich Schiller University in Jena supported in part by the DFG Grants INST 275/334-1 FUGG and INST 275/363-1 FUGG. The work of J. J. L. was partly supported by the UKRI Sci- ence and Technology Facilities Council (STFC) Research Software Engineering Fellowship EP/V052489/1 and by the Supercomputing Wales project, which is part-funded by the European Regional Development Fund (ERDF) via Welsh Government.