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 T0ā of the Polyakov loop potential. Under the
constraints that magnetic catalysis is realized at zero temperature and the
chiral transition at B=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.Comment: 8 pages, 5figure