Thermo-magnetic effects in quark matter: Nambu--Jona-Lasinio model   constrained by lattice QCD
  The phenomenon of inverse magnetic catalysis of chiral symmetry in QCD predicted by lattice simulations can be reproduced within the Nambu--Jona-Lasinio model if the coupling~$G$ of the model decreases with the strength $B$ of the magnetic field and temperature~$T$. The thermo-magnetic dependence of $G(B,T)$ is obtained by fitting recent lattice QCD predictions for the chiral transition order parameter. Different thermodynamic quantities of magnetized quark matter evaluated with $G(B, T)$ are compared with the ones obtained at constant coupling, $G$. The model with $G(B,T)$ predicts a more dramatic chiral transition as the field intensity increases. In addition, the pressure and magnetization always increase with $B$ for a given temperature. Being parametrized by four magnetic field dependent coefficients and having a rather simple exponential thermal dependence our accurate ansatz for the coupling constant can be easily implemented to improve typical model applications to magnetized quark matter. 
R. L. S. Farias, V. S. Timoteo, S. S. Avancini, M. B. Pinto and G.   Krein
hep-ph hep-lat nucl-th