Three-dimensional Gross–Neveu model at nonzero temperature and in an external magnetic field

The phase structure of the $(2+1)$ Gross–Neveu model at nonzero temperature $T$ and in an external field $H$ is studied in the leading order of the $1/N$ expansion. It is shown that for any fixed value of $T$ there exists a critical value $H_c$ of the magnetic field such that when $H>H_c$ the chiral invariance of the model is spontaneously broken. For fixed $H$, there exists a critical value of the temperature $T_c(H)$ such that for $T>T_c(H)$ the original symmetry of the model is restored. The phase portrait of the model is constructed in the $H-T$ plane.