  The phase diagram and thermodynamic properties of the (2+1)-dimensional
Gross-Neveu model are studied in the presence of a constant magnetic field. The
optimized perturbation theory (OPT) is used to obtain results going beyond the
large-N approximation. The free energy and the complete phase diagram of the
model, in terms of temperature, chemical potential and magnetic field are
obtained and studied in details. By comparing the results from the OPT and the
large-N approximation, we conclude that finite N effects favor the phenomenon
of inverse magnetic catalysis when the coupling constant is negative. We show
that with the OPT the value of the coexistence chemical potential at vanishing
temperature always decreases with the magnetic field. This is opposite to what
is seen in the large-N approximation, where for large magnetic fields the
coexistence chemical potential starts again to increase. Likewise, at finite
temperature, the value of the chemical potential at the tricritical point also
decreases with the magnetic field in the OPT case. Consequently, the shape of
the phase diagrams predicted by the OPT and by the large-N approximation look
very different in the presence of high magnetic fields. Finally, for small
values of magnetic field and temperature, we identify the presence of possible
intermediate nonchiral phase transitions when varying the chemical potential.
We show that these phenomena are not an artifact of the large-N approximation
and that they also occur within the OPT framework. These intermediate
transitions are interpreted to be a consequence of the de Haas--van Alphen
oscillations. We also explain why this type of phenomenon can happen in general
for negative couplings but not for positive couplings.
