Percolation and Deconfinement in SU(2) Gauge Theory

Abstract

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.