  Based on the trace anomaly for the energy-momentum tensor, an effective
theory for the thermodynamics of the deconfining phase, and by assuming the
asymptotic behavior to be determined by one-loop perturbation theory we compute
the nonperturbative beta function for the fundamental coupling $g$ in SU(2) and
SU(3) Yang-Mills theory. With increasing temperature we observe a very rapid
approach to the perturbative running. The Landau pole is nonperturbatively
screened.
