One-loop omega-potential of charged massive particles in a constant   homogeneous magnetic field at high temperatures
  The explicit expressions for the high-temperature expansions of the one-loop corrections to the omega-potential coming from charged scalar and Dirac particles and, separately, from antiparticles in a constant homogeneous magnetic field are derived. The explicit expressions for the non-perturbative corrections to the effective action at finite temperature and density are obtained. Thermodynamic properties of a gas of charged scalars in a constant homogeneous magnetic field are analyzed in the one-loop approximation. It turns out that, in this approximation, the system suffers a first-order phase transition from the diamagnetic to the superconducting state at sufficiently high densities. The improvement of the one-loop result by summing the ring diagrams is investigated. This improvement leads to a drastic change in thermodynamic properties of the system. The gas of charged scalars passes to the ferromagnetic state in place of the superconducting one at high densities and sufficiently low temperatures, in the high temperature regime. 
I.S. Kalinichenko, P.O. Kazinski
hep-th