Effective actions for finite temperature Lattice Gauge Theories

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