Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm

We give a simple explanation of the Swendsen-Wang algorithm for Potts models in terms of a joint model of Potts spin variables interacting with bond occupation variables. We then show how to generalize this representation, as well as the corresponding Monte Carlo algorithm, to arbitrary models. We give initial results of tests of the new algorithm on the two-dimensional XY model.