Three-dimensional Gross–Neveu model in an external magnetic field. I

In the leading order of the $1/N$ expansion, the (2 + l)-dimensional Gross–Neveu model in a constant external magnetic field is considered. It is shown that for $g>0$ ($g$ is the coupling constant) and arbitrarily small value of $H$ the chiral invariance of the model is spontaneously broken. For $g<0$, the symmetry, broken at $H=0$, is not restored at any arbitrarily large value of the external magnetic field.