  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.
