3-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 temperature T and in the presence of an external electromagnetic field. The major results are as follows: 1. At T = 0, H not-equal 0 (a magnetic field), the original symmetry of the model breaks for any H values. 2. At T = 0, E not-equal 0 (an electric field) an E(c) is shown to exist, such that for E < E(c) the original symmetry is broken, but for E > E(c) the vacuum of the model is symmetric. 3. At T not-equal 0, H not-equal 0, and at a fixed T value such an H(c)(T) is shown to exist that for H > H(c)(T) the chiral invariance of the model is spontaneously broken. For any fixed H value there exists such an T(c)(H) that for T > T(c)(H) the symmetry restores. The phase portrait of the model is drawn.