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.