Discrete symmetry breaking and restoration at finite temperature in 3D Gross-Neveu model

Dynamical spontaneous breaking of some discrete symmetries including special parities and time reversal and their restoration at finite temperature T are researched in 3D Gross-Neveu model by means of Schwinger-Dyson equation in the real-time thermal field theory in the fermion bubble diagram approximation. When the momentum cut-off Λ is large enough, the equation of critical chemical potential μc and critical temperature Tc will be Λ-independent and identical to the one obtained by auxiliary scalar field approach. The dynamical fermion mass m≡m(T,μ), as the order parameter of symmetry breaking, has the same (Tc−T)1/2 behavior at T≲Tc as one in 4D NJL-model and this shows the second-order phase transition feature of the symmetry restoration at T>Tc. It is also proven that no scalar bound state could exist in this model.