  We study inverse magnetic catalysis in the Nambu--Jona-Lasinio model beyond
mean field approximation. The feed-down from mesons to quarks is embedded in an
effective coupling constant at finite temperature and magnetic field. While the
magnetic catalysis is still the dominant effect at low temperature, the meson
dressed quark mass drops down with increasing magnetic field at high
temperature due to the dimension reduction of the Goldstone mode in the
Pauli-Villars regularization scheme.
