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 ${\sigma }_s=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}{g}^4(T)T^2$. We investigate below what happens when one imposes in addition constant magnetic field and discover remarkable structure of the resulting thermodynamic potential.