Phase diagram in an external magnetic field beyond a mean-field approximation

Abstract

The phase structure of the Polyakov loop-extended chiral quark-meson model is explored in a nonperturbative approach, beyond a mean-field approximation, in the presence of a magnetic field. We show that by including meson fluctuations one cannot resolve the qualitative discrepancy on the dependence of the crossover transition temperature in a nonzero magnetic field between effective model predictions and recent lattice results [1]. We compute the curvature of the crossover line in the $T\ensuremath{-}{\ensuremath{\mu}}_{B}$ plane at a nonzero magnetic field and show that the curvature increases with increasing magnetic field. On the basis of QCD inequalities, we also argue that, at least in the large ${N}_{c}$ limit, a chiral critical end point and, consequently, a change from crossover to a first-order chiral phase transition are excluded at zero baryon chemical potential and nonzero magnetic field.