Inverse magnetic catalysis in the (2+1)-flavor Nambu--Jona-Lasinio and   Polyakov--Nambu--Jona-Lasinio models
  The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor Nambu--Jona-Lasinio (NJL) model and the NJL model with the Polyakov loop (PNJL). A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows to reproduce the lattice QCD results with respect to the quark condensates and Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high temperatures and suppressed for temperatures close to the transition temperatures and the Polyakov loop increases with the magnetic field. 
M. Ferreira, P. Costa, O. Louren\c{c}o, T. Frederico, and C.   Provid\^encia
hep-ph