  The thermodynamics of pure glue theories can be described in terms of an
effective action for the Polyakov loop. This effective action is of the
Landau-Ginzburg type and its variables are the angles parametrizing the loop.
In this paper we compute perturbative corrections to this action. Remarkably,
two-loop corrections turn out to be proportional to the one-loop action,
independent of the eigenvalues of the loop. By a straightforward generalization
of the 't Hooft coupling this surprisingly simple result holds for any of the
classical and exceptional groups.
