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

Abstract

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 χ B to compare with the other two susceptibilities χ c (chiral susceptibility) and χ 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.

Inverse magnetic catalysis and confinement within a contact interaction model for quarks

“…Thus, fermion and antifermion pairs are closer together on the average, facilitating the formation of a chiral condensate, the so-called magnetic catalysis effect [25,26] (see [27] for a recent review). This phenomenon is universal and has been explored in NJL models [28,29,30,31,32,33,34], QED [35,36,37,38,39,40,41] and QCD [42,43,44] among other theories and under a variety of external circumstances like a thermal bath, in low and high dimensions, finite density and so on. In QCD, it is observed an increase of the pseudo-critical transition temperatures as the strength of the magnetic field grows bigger [45].…”

Chiral Chemical Potential and Magnetic Effects on QCD Matter in NJL Model with a Self-Consistent Method

“…There are two reasons. Firstly, some results depend on the sign of the electric charge of quark, so a 1-flavor NJL model with an arbitrary electric charge can clearly demonstrate the dependency; secondly, the gap equations and some results of the 1-flavor NJL model can be easily generalized to the cases of 2-flavor, because the fermion propagator of 2-flavor (u, d quarks) is the equivalent to a direct sum of u quark propagator and d quark propagator with the mean-field approximation [36]. Therefore, using the 1-flavor NJL model can keep the discussions and deductions concise.…”

Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD

“…[43,163,164,165,166,167,168,169,170,171,172]. In the following, we take the NJL model, which is successful as well as popular in chiral phase transition studies [173,174,175,176,177,178,179,161,180,181,182], as an example, and give some discussions on the applications of some susceptibilities [36], similar discussions with in the framework of QED 3 can be found in Ref. [183].…”