Swendsen–Wang algorithm: Difference between revisions

Revision as of 06:39, 15 July 2025

Revision as of 19:19, 18 July 2025

Line 1:

The '''Swendsen–Wang algorithm''' is the first non-local or cluster [[algorithm]] for [[Monte Carlo simulation]] for large systems near [[Critical point (thermodynamics)|criticality]]. It has been introduced by [[Robert Swendsen]] and [[Jian-Sheng Wang]] in 1987 at [[Carnegie Mellon University|Carnegie Mellon]].

The original algorithm was designed for the [[Ising model|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|Potts]] model through percolation models of connecting bonds, due to Fortuin and Kasteleyn. It has been generalized by Barbu and Zhu<ref>{{Cite journal|last1=Barbu|first1=Adrian|last2=Zhu|first2=Song-Chun|date=August 2005|title=Generalizing Swendsen-Wang to sampling arbitrary posterior probabilities|url=https://pubmed.ncbi.nlm.nih.gov/16119263/|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1239–1253|doi=10.1109/TPAMI.2005.161|issn=0162-8828|pmid=16119263|s2cid=410716}}</ref> to arbitrary sampling probabilities by viewing it as a [[Metropolis–Hastings algorithm]] and computing the acceptance probability of the proposed Monte Carlo move.

== Motivation ==