Inverse magnetic catalysis and regularization in the quark-meson model

Motivated by recent work on inverse magnetic catalysis at finite temperature, we study the quark-meson model using both dimensional regularization and a sharp cutoff. We calculate the critical temperature for the chiral transition as a function of the Yukawa coupling in the mean-field approximation varying the renormalization scale and the value of the ultraviolet cutoff. We show that the results depend sensitively on how one treats the fermionic vacuum fluctuations in the model and in particular on the regulator used. Finally, we explore a $B$-dependent transition temperature for the Polyakov loop potential $T_0(B)$ using the functional renormalization group. These results show that even arbitrary freedom in the function $T_0(B)$ does not allow for a decreasing chiral transition temperature as a function of $B$. This is in agreement with previous mean-field calculations.