On generation of Abelian magnetic fields in SU(3) gluodynamics at high temperature

The vacuum state of SU(3) gluodynamics at high temperature is investigated. A consistent approach including the calculation of either the spontaneously generated constant chromomagnetic isotopic $H_{3}$ and hypercharge $H_{8}$ fields or the polarization operator of charged gluons in this background is applied. It is shown within the effective potential including the one-loop plus daisy diagrams that the specific values of the fields deliver a global minimum to free energy. The spectrum of the transversal charged modes is stable at high temperature due to a gluon magnetic mass accounting for the vacuum fields. This leads to stable chromomagnetic fields in the deconfinement phase of QCD. A comparison with the results of other approaches is done.