Three-dimensional Gross-Neveu model at nonzero temperature and in the presence of an external electromagnetic field

The phase structure of the (2+1)-dimensional Gross-Neveu model is considered at a nonzero temperatureT and in the presence of an external electromagnetic field. The major results are as follows: 1. AtT=0,H0 (a magnetic field), the original symmetry of the model breaks for anyH values. 2. AtT=0,E0 (an electric field) anE_c is shown to exist, such that forEE_c the original symmetry is broken, but forE>E_c the vacuum of the model is symmetric. 3. AtT0,H0, and at a fixedT value such anH_c(T) is shown to exist that forH>H_c(T) the chiral invariance of the model is spontancously broken. For any fixedH value there exists such anT_c(H) that forT>T_c(H) the symmetry restores. The phase portrait of the model is drawn.