Chiral Transition Within Effective Quark Models Under Magnetic Fields
  We consider the simplest versions of the Nambu--Jona-Lasinio (NJL) model and the Linear Sigma Model (LSM), in the Mean Field Approximation (MFA), in order to analyze hot and dense two flavor quark matter subject to strong magnetic fields. We pay especial attention to the case of a finite chemical potential, which has not yet been fully explored. Our results, for the NJL model, are in qualitative agreement with other recent applications showing that, for stronger fields, the first order segment of the transition line increases with the magnetic strength while the coexistence chemical potential value, at low temperatures, decreases. In the present work, one of the most important results is related to the analysis of how these features affect the phase coexistence region in the $T-\rho_B$ plane. We find that the coexistence boundary oscillates around the B=0 value for magnetic fields of the order $eB \lesssim 9.5\, m_\pi^2$ which can be understood by investigating the filling of Landau levels at vanishing temperature. So far, most investigations have been concerned with the effects of the magnetic field over the $T-\mu$ plane only while other thermodynamical quantities such as the adiabats, the quark number susceptibility, the interaction measure and the latent heat have been neglected. Here, we take a step towards filling this gap by investigating the influence of a magnetic field over these quantities. Finally, we argue that a naive application of the MFA does not seem to be appropriate to treat the LSM in the presence of magnetic fields. 
Gabriel N. Ferrari, Andre F. Garcia and Marcus B. Pinto
hep-ph nucl-th