  Cluster percolation and second order thermal phase transitions show an
amazing number of common features: power laws of the variables at criticality,
scaling relations of the critical exponents and universality of the critical
indices. Because of that, percolation theory seems to be an ideal framework to
devise a geometrical picture of a second order phase transition; the leading
characters of the phenomenon are ordered domains, whose size increases while
approaching the threshold until they fuse into a spanning structure, so that
the order from local becomes global. Such a geometrical picture is known to be
successful in the Ising model. The clusters are site-bond clusters, i.e. they
are built by joining nearest-neighbouring aligned spins with some
temperature-dependent bond probability. In this work we extend this result to a
wide variety of theories, from continuous Ising-like models to O(n) models. On
the grounds of these results, we devise a percolation picture for the confining
phase transition of SU(2) pure gauge theory, exploiting its analogies with the
Ising model. The cluster definition is obtained by constructing suitable
effective theories for SU(2), which admit an equivalent percolation
formulation.
