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

TL;DR

This paper investigates how discrete symmetries are broken and restored at finite temperature in the 3D Gross-Neveu model using Schwinger-Dyson equations, revealing second-order phase transition characteristics.

Contribution

It demonstrates the symmetry breaking and restoration in the 3D Gross-Neveu model at finite temperature, with critical parameters independent of the cutoff and confirms the second-order phase transition behavior.

Findings

Critical temperature and chemical potential are cutoff-independent.

Fermion mass exhibits a (T_c - T)^{1/2} behavior near T_c.

No scalar bound states exist in the model.

Abstract

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 $\Lambda$ is large enough, the equation of critical chemical potential $\mu_c$ and critical temperature $T_c$ will be $\Lambda$-independent and identical to the one obtained by auxialiary scalar field approach. The dynamical fermion mass m, as the order parameter of symmetry breaking, has the same $(T_c-T)^{1/2}$ behavior as one in 4D NJL-model when T is less than and near $T_c$ and this shows the second-order phase transition feature of the symmetry restoration at $T>T_c$. It is also proven that no scalar bound state could exist in this model.