Studies of Wigner-Weyl solution and external magnetic field in an NJL model

In this paper, we explore the dynamical chiral symmetry breaking by employing a two-flavor Nambu-Jona-Lasinio (NJL) model with constant external magnetic field. After changing the coupling strength of the NJL model, we found that the Wigner-Weyl solution and Nambu-Goldstone solution of the gap equation could coexist. Even though the gap equation only has Nambu-Goldstone solution at zero temperature, the Wigner-Weyl solution may appear when magnetic field strength and temperature are nonzero. For the Nambu-Goldstone solution, magnetic field and temperature have opposite impact on the chiral dynamical mass. In the chiral limit, the magnetic field dependence of chiral dynamical mass reveals the existence of inverse magnetic catalysis for the Wigner-Weyl solution. However, the two phases have different responses to the magnetic field and temperature in the chiral limit but the same beyond chiral limit. Furthermore, the order of the transition from the Nambu-Goldstone phase to Wigner-Weyl phase depends on the choice of model parameters. We have also calculated the susceptibilities of dynamical mass with respect to the temperature.