Phase diagram of the magnetized planar Gross-Neveu model beyond the large-N approximation

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. We find that some of the main qualitative changes induced by the OPT finite N corrections concern the region of intermediate to high chemical potentials where this approximation adds a term proportional to lambda <psi(+) psi >(2)/N to the free energy. Then, depending on the sign of lambda (relative to the critical coupling) and magnitude of the magnetic field, we observe a weakening (when lambda < 0) or enhancement (when lambda > 0) of the chiral broken region in the magnetized fermionic system. 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 tends to decrease for large values of 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.