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 fieldB. 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 parameterT0of the Polyakov loop potential. Under the constraints that magnetic catalysis is realized at zero temperature and the chiral transition atB=0is 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.
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