Swendsen and Wang derived their algorithm from a simple relation which transforms a Potts spin model into a bond percolation model. What is percolation?
Suppose we have a two-dimensional lattice of sites, and we put a bond between every pair of neighboring sites with probability p. Sites are then bonded together into connected clusters. \
At a critical value of p, will get percolation, i.e., one cluster will span the lattice, meaning that there is a connected path across the lattice through a single spanning cluster. For an infinite two-dimensional lattice, .