Stabilization of Chromomagnetic Fields at High Temperature?

It is well known that a tachyonic mode appears in the spectrum of Yang—Mills theory with a static uniform magnetic field, and that the free energy has an (unstable) minimum at finite magnetic field. It is argued that spontaneous generation of magnetic field does not take place at high temperature due to nonperturbative magnetic screening. Furthermore, the dispersion relation for gauge field fluctuations in an external magnetic field at high temperature is solved. The lowest energy mode is stable against spontaneous generation of magnetic fields since it acquires a thermal mass. However, the resummed free energy (by necessity computed in the imaginary time formalism) still shows an instability, unaffected by the resummation, since the self-energy is vanishing at static Matsubara frequency.