EFFECTIVE COUPLING-CONSTANTS IN GAUGE-THEORIES AT HIGH-TEMPERATURE

High temperature behavior of the effective gauge coupling constants, d efined through the effective Lagrangians L(H, T) of strong magnetic fi eld H = const, is investigated for a number of models. In spinor QED t he well-known zero charge behavior is realized in the limit T much gre ater than (gH)(1/2) > mu, mu is subtraction point in the field. In sca lar QED in addition to logarithmic term similar to In T/T-0 describing the zero charge, the term similar to T/(gH)(1/2) appears and dominate s at high temperatures. Similar terms are also present in the non-Abel ian models and spoil asymptotic freedom of perturbative vacuum. In the latter models, the linear in T terms are resulted in the generation o f classical homogeneous magnetic fields. At this background asymptotic freedom is restored.