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.