  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 non-zero magnetic field between effective
model predictions and recent lattice results (arXiv:1111.4956).We compute the
curvature of the crossover line in the T - {\mu}_B plane at a non-zero 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 Nc
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 non-zero magnetic field.
