Mean-field approximation for Abelian and non-Abelian lattice gauge theories at finite temperature

The phase diagrams of the Z(2), Z(3), and SU(2) four-dimensional lattice gauge theories at finite temperature are analyzed by the mean-field technique including Gaussian corrections. The effect of the finite size of the lattice in the time Euclidean direction is considered at lowest order by the Bethe-Peierls approximation. We discuss the gauge dependence of the results. The predictions for Abelian models are excellent but for SU(2) we show that in order to reproduce the Monte Carlo--simulations results, the Gaussian corrections are not enough and higher-loop calculations may be necessary