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

Song Shi, You-Chang Yang, Yong-Hui Xia, Zhu-Fang Cui, Xiao-Jun Liu, Hong-Shi Zong

Published 2015-03-02Version 1

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.