Effective actions for finite temperature Lattice Gauge Theories.

We consider a lattice gauge theory at finite temperature in (d + 1) dimensions with the Wilson action and different couplings beta(t) and beta(s) for timelike and spacelike plaquettes. By using the character expansion and Schwinger Dyson type equations we construct, order by order in beta(s), an effective action for the Polyakov loops which is exact to all orders in beta(t). As an example we construct the first non-trivial order in beta(s) for the (3+1) dimensional SU(2)model and use this effective action to extract the deconfinement temperature of the model.