A search for inverse magnetic catalysis in thermal quark–meson models

We explore the parameter space of the two-flavor thermal quark–meson model and its Polyakov loop-extended version under the influence of a constant external magnetic field B  . We investigate the behavior of the pseudo critical temperature for chiral symmetry breaking taking into account the likely dependence of two parameters on the magnetic field: the Yukawa quark–meson coupling and the parameter T0T0 of the Polyakov loop potential. Under the constraints that magnetic catalysis is realized at zero temperature and the chiral transition at B=0B=0 is a crossover, we find that the quark–meson model leads to thermal magnetic catalysis for the whole allowed parameter space, in contrast to the present picture stemming from lattice QCD.