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.