Quark matter under strong magnetic fields in SU(2) NJL-type models: parameter dependence of the cold dense matter phase diagram

The phase structure of magnetized cold quark matter is analyzed in the framework of the two-flavor Nambu-Jona-Lasinio models paying special attention to its dependence on the model parameters as different values within the phenomenological allowed range are considered. We first discuss the simpler chiral limit case, and then the more realistic situation of finite current masses. We show that in spite of the difference in the nature of some transitions, both cases are alike and exhibit a rather rich phase structure for a significant range of acceptable parameters. A simplification of the phase structure is obtained as parameters leading to larger values of the dressed quark mass in the vacuum are considered. Finally, we consider the so-called "inverse catalysis effect" showing that in some phases it implies an actual decrease of the order parameter as the magnetic field increases.