Mean field for topological excitations of Z2 spin and gauge models

A mean field approach for the disorder parameters is obtained by applying the duality transformation to a Bethe-Peierls type approximation which involves finite clusters. Applications to Z₂ models with global and local symmetries are discribed and systematical improvements are obtained by considering clusters of increasing size. For gauge theories a manifestly gauge-invariant mean field is obtained: the phenomenology of the spontaneous symmetry breaking is reproduced by considering the suitable order parameters and the standard mean field for gauge theories in four dimensions is reinterpreted.