  The thermodynamic properties of an ideal gas of charged vector bosons (with mass m and charge e) is studied in a strong external homogeneous magnetic field no greater than the critical value B_{cr}=m^2/e. The thermodynamic potential, after appropriate analytic continuation, is then used in the study of the spontaneous production of charged spin-one boson pairs from vacuum in the presence of a supercritical homogeneous magnetic field at finite temperature. 
Pair Production of charged vector bosons in supercritical magnetic   fields at finite temperatures