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Next: The Swendsen-Wang Algorithm Up: Other Monte Carlo Previous: The Potts Model

Percolation

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, .



Paul Coddington, Northeast Parallel Architectures Center at Syracuse University, paulc@npac.syr.edu