Thermal versus vacuum magnetization in QED

The magnetized relativistic Fermi (spin-1/2) and Bose (spin-0) gases are studied at finite temperature and density. At high enough magnetic fields the renormalized, paramagnetic vacuum (T=μ=0) contribution starts to dominate the magnetization in both cases. This happens when the thermal magnetization saturates in the Fermi case, and when the thermal magnetization changes from a diamagnetic to a paramagnetic behavior in the Bose case. For fermions at high temperatures, the nonlinear vacuum part of the effective action is completely canceled by terms in the thermal effective action, so that the effective action becomes quadratic in the field. In the Bose case such a cancellation does not occur. Furthermore, we find for the Bose gas that the effective coupling constant for a weak nonzero external magnetic field is a decreasing function of the temperature