Magnetic catalysis and inverse magnetic catalysis in QCD

We investigate the effects of strong magnetic fields on the QCD phase structure at vanishing density by solving the gluon and quark gap equations, and by studying the dynamics of the quark scattering with the four-Fermi coupling. The chiral crossover temperature as well as the chiral condensate are computed. For asymptotically large magnetic fields we find magnetic catalysis, while we find inverse magnetic catalysis for intermediate magnetic fields. Moreover, for large magnetic fields the chiral phase transition for massless quarks turns into a crossover. The underlying mechanisms are then investigated analytically within a few simplifications of the full numerical analysis. We find that a combination of gluon screening effects and the weakening of the strong coupling is responsible for the phenomenon of inverse catalysis. In turn, the magnetic catalysis for large magnetic fields is already indicated by simple arguments based on dimensionality.