Nonperturbative QCD thermodynamics in the external magnetic field

The thermodynamics of quarks and gluons strongly depends on the vacuum colormagnetic field, which grows with the temperature T, so that spatial string tension (sigma _s =mathrm{const}~ g^4 (T) T^2). We investigate below what happens when one imposes in addition constant magnetic field and discover remarkable structure of the resulting thermodynamic potential.