We perform a lattice study of the (2+1)-dimensional Gross-Neveu model in a background magnetic field B and at non-zero chemical potential μ. The complex-action problem arising in our simulations using overlap fermions is under control. For B=0 we observe a first-order phase transition in μ even at non-vanishing temperatures. Our main finding, however, is that the rich phase structure found in the limit of infinite flavor number Nf is washed out by the fluctuations present at Nf=1. We find no evidence for inverse magnetic catalysis, i.e., the decrease of the order parameter of chiral symmetry breaking with B for μ close to the chiral phase transition. Instead, the magnetic field tends to enhance the breakdown of chiral symmetry for all values of μ below the transition. Moreover, we find no trace of spatial inhomogeneities in the order parameter. We briefly comment on the potential relevance of our results for QCD. If you use this software, please cite the corresponding paper: https://doi.org/10.48550/arXiv.2304.14812 (or better the not-yet-existing published version)

This work has been funded by the Deutsche Forschungsgemein- schaft (DFG) under Grant No. 406116891 within the Research Training Group RTG 2522/1. The work of J. J. L. was supported by the UKRI Science 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 Govern- ment. The simulations 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, as well as on the Swansea University SUNBIRD cluster (part of the Supercomputing Wales project). The Swansea University SUNBIRD system is part funded by the European Regional Development Fund (ERDF) via Welsh Government.