Dynamical chiral symmetry breaking in the NJL model with a constant external magnetic field

TL;DR

This paper introduces a new method to analyze dynamical chiral symmetry breaking in the NJL model under a constant magnetic field, revealing phase transition behaviors and susceptibilities at various conditions.

Contribution

Develops a novel approach to derive the fermion propagator in magnetic fields and studies phase transitions and susceptibilities in the NJL model with external magnetic fields.

Findings

Phase diagram between magnetic field and temperature

Crossover transition when current mass is non-zero

Second order phase transition in the chiral limit

Abstract

In this paper we develop a new method that is different from Schwinger proper time method to deduce the fermion propagator with a constant external magnetic field. In the NJL model, we use this method to find out the gap equation at zero and non-zero temperature, and give the numerical results and phase diagram between magnetic field and temperature. Beside these, we also introduce current mass to study the susceptibilities, because there is a new parameter (the strength of external magnetic field) in this problem, corresponding this new parameter, we have defined a new susceptibility $\chi_B$ to compare with the other two susceptibilities $\chi_c$ (chiral susceptibility) and $\chi_T$ (thermal susceptibility), and all of the three susceptibilities show than when current mass is not zero, the phase transition is a crossover, while for comparison, in the chiral limit, the susceptibilities show a second order phase transition. At last, we give out the critical coefficients of different susceptibilities in the chiral limit.