We study the physical mechanism of how an external magnetic field influences
the QCD quark condensate. Two competing mechanisms are identified, both relying
on the interaction between the magnetic field and the low quark modes. While
the coupling to valence quarks enhances the condensate, the interaction with
sea quarks suppresses it in the transition region. The latter `sea effect' acts
by ordering the Polyakov loop and, thereby, reduces the number of small Dirac
eigenmodes and the condensate. It is most effective around the transition
temperature, where the Polyakov loop effective potential is flat and a small
correction to it by the magnetic field can have a significant effect. Around
the critical temperature, the sea suppression overwhelms the valence
enhancement, resulting in a net suppression of the condensate, named inverse
magnetic catalysis. We support this physical picture by lattice simulations
including continuum extrapolated results on the Polyakov loop as a function of
temperature and magnetic field. We argue that taking into account the increase
in the Polyakov loop and its interaction with the low-lying modes is essential
to obtain the full physical picture, and should be incorporated in effective
models for the description of QCD in magnetic fields in the transition region.Comment: 19 pages, 8 figures, new reference added, version accepted for
publicatio