  Thermodynamics of the three-flavor quark-meson model with axial anomaly is
studied in the presence of external magnetic fields. The nonperturbative
functional renormalization group is employed in order to incorporate quantum
and thermal fluctuations beyond the mean-field approximation. We calculate the
magnetic susceptibility with proper renormalization and find that the system is
diamagnetic in the hadron phase and paramagnetic in the hot plasma phase. The
obtained values of the magnetic susceptibility are in reasonable agreement with
the data from first-principle lattice QCD. Comparison with the mean-field
approximation, the Hadron Resonance Gas model and a free gas with
temperature-dependent masses is also made.
