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 <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math> of the Polyakov loop potential. Under the constraints that magnetic catalysis is realized at zero temperature and the chiral transition at <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mn>0</mn></math> 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