Strong magnetic fields and QCD: inverse magnetic catalysis, the phase transition and the equation of state

Magnetic field strengths created in solid state physics laboratory
experiments do not exceed 10^6 Gauss. Much stronger fields can be present
in compact astrophysical objects. For instance near the surface of a
magnetar these can reach values as high as 10^{15} Gauss, with even higher
values towards the core.

Recently, it was realized that in heavy ion collisions at the Brookhaven
National Lab as well as at the Large Hadron Collider at CERN even larger
field strengths are being generated, for very short periods of time,
in very small volumes. These magnetic fields are so strong that in their
presence even some properties of strongly interacting matter, composed of
quarks and gluons, will change, possibly with observable consequences.

I will describe theoretical expectations relating to matter in such
environments. These have mostly been obtained by simulating quantum
chromodynamics on a spacetime lattice on supercomputers.