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arXiv · 1503.00452

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
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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 $χ_B$ to compare with the other two susceptibilities $χ_c$ (chiral susceptibility) and $χ_T$ (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.

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Song Shi, You-Chang Yang, Yong-Hui Xia, Zhu-Fang Cui, Xiao-Jun Liu, Hong-Shi Zong. 2015-03-02. Dynamical chiral symmetry breaking in the NJL model with a constant external magnetic field. https://doi.org/10.1103/physrevd.91.036006

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