Swendsen–Wang algorithm
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The Swendsen–Wang algorithm is the first non-local or cluster algorithm for Monte Carlo simulation for large systems near criticality. It has been introduced by Robert Swendsen and Jian-Sheng Wang in 1987 at Carnegie Mellon.
The original algorithm was designed for the Ising and Potts models, and it was later generalized to other systems as well, such as the XY model by Wolff algorithm and particles of fluids. The key ingredient was the random cluster model, a representation of the Ising or Potts model through percolation models of connecting bonds, due to Fortuin and Kasteleyn. It has been generalized by Barbu and Zhu[1] to arbitrary sampling probabilities by viewing it as a Metropolis–Hastings algorithm and computing the acceptance probability of the proposed Monte Carlo move.