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The phenomenon of inverse magnetic catalysis of chiral symmetry in QCDpredicted by lattice simulations can be reproduced within theNambu--Jona-Lasinio model if the coupling~$G$ of the model decreases with thestrength $B$ of the magnetic field and temperature~$T$. The thermo-magneticdependence of $G(B,T)$ is obtained by fitting recent lattice QCD predictionsfor the chiral transition order parameter. Different thermodynamic quantitiesof magnetized quark matter evaluated with $G(B, T)$ are compared with the onesobtained at constant coupling, $G$. The model with $G(B,T)$ predicts a moredramatic chiral transition as the field intensity increases. In addition, thepressure and magnetization always increase with $B$ for a given temperature.Being parametrized by four magnetic field dependent coefficients and having arather simple exponential thermal dependence our accurate ansatz for thecoupling constant can be easily implemented to improve typical modelapplications to magnetized quark matter.

Thermo-magnetic effects in quark matter: Nambu--Jona-Lasinio model constrained by lattice QCD