Thermodynamic Gross-Neveu model in a constant electromagnetic field Original Research Article

We analyze the effective potential of the D-dimensional thermodynamic Gross-Neveu model (defined by large-N leading order, 2 ⩽ D < 4) in a constant electromagnetic field (E · B = 0). The potential is derived from a thermal analogy of the worldline formalism. In the magnetic case, the potential is expressed in terms of a discretized momentum sum instead of a continuum momentum integral, and it reproduces the known critical values of μ and T in the continuum limit. In the electric case, chiral symmetry is restored at finite T (with arbitrary μ) against instability of the fermion vacuum. An electromagnetic duality is pointed out as well. Phase diagrams are obtained in both cases.