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 − ρB plane. We find that the coexistence boundary oscillates around the B = 0 value for magnetic fields of the order eB < ∼ 9.5 m 2 π 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 − µ 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.

Lattice QCD results for the coefficient c2 appearing in the Taylor expansion of the pressure show that this quantity raises with the temperature towards the Stefan-Boltzmann limit. On the other hand, model approximations predict that when a vector repulsion, parametrized by GV , is present this coefficient reaches a maximum just after Tc and then deviates from the lattice predictions. Recently, this discrepancy has been used as a guide to constrain the (presently unknown) value of GV within the framework of effective models at large-Nc (LN). In the present investigation we show that, due to finite Nc effects, c2 may also develop a maximum even when GV = 0 since a vector repulsive term can be dynamically generated by exchange type of radiative corrections. Here we apply the the Optimized Perturbation Theory (OPT) method to the two flavor Polyakov-NambuJona-Lasinio model (at GV = 0) and compare the results with those furnished by lattice simulations an by the LN approximation at GV = 0 and also at GV = 0. The OPT numerical results for c2 are impressively accurate for T 1.2 Tc but, as expected, predict that this quantity develops a maximum at high-T . After identifying the mathematical origin of this extremum we argue that such a discrepant behavior may naturally arise within these effective quark models (at GV = 0) whenever the first 1/Nc corrections are taken into account. We then interpret this hypothesis as an indication that beyond the large-Nc limit the correct high temperature (perturbative) behavior of c2 will be faithfully described by effective models only if they also mimic the asymptotic freedom phenomenon.

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with YangMills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasi-particle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

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The determination of the critical point on the QCD phase diagram depends experimentally on thermodynamic quantities related to the cumulants of the pressure. These quantities appear as coefficients in the Taylor expansion of the pressure and, specifically for the second order cumulant c 2, QCD results on the lattice (LQCD) show that it raises with the temperature towards the Stefan-Boltzmann limit. On the other hand, when one evaluates c 2 within quark effective models considering a repulsion on the vector channel parametrized by GV , this observable reaches a maximum just after Tc , deviating itself from LQCD predictions. Here we apply the Optimized Perturbation Theory (OPT) method to the two flavor Polyakov–Nambu–Jona-Lasinio model (at GV = 0) to confront our results with those furnished by LQCD simulations. We show that c 2 behaves satisfactorily at low-T and close to Tc , but, with GV ≠ 0, it develops a maximum at high-T. Our conclusions indicate that it would be possible that the correct high temperature behavior of c 2 beyond LN limit could be properly achieved by effective quark models if they also mimic the so-called asymptotic freedom phenomenon.