Shi, S (reprint author), Nanjing Univ, Inst Acoust, Key Lab Modern Acoust, MOE, Nanjing 210093, Jiangsu, Peoples R China.
In this paper, we develop a new method that is different from the 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 the gap equation at zero and nonzero temperature and give the numerical results and phase diagram between the magnetic field and temperature. Additionally, we introduce the current mass to study the susceptibilities because there is a new parameter (the strength of the external magnetic field) in this problem. Corresponding to this new parameter, we define a new susceptibility X-B to compare with the other two susceptibilities Xc (chiral susceptibility) and X-T (thermal susceptibility). All three susceptibilities show that when the 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. Last, we give the critical coefficients of different susceptibilities in the chiral limit.
National Natural Science Foundation of China [11275097, 11475085, 11265017]
; China Postdoctoral Science Foundation [2014M561621]
; Jiangsu Planned Projects for Postdoctoral Research Funds [1401116C, 1402006C]
; National Basic Research Program of China [2012CB921504]
; Guizhou province outstanding youth science and technology talent cultivation object special funds [QKHRZ(2013)28]