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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|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|bibcode=2005ITPAM..27.1239B |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 ==
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*{{cite journal | last1=Fortuin | first1=C.M. | last2=Kasteleyn | first2=P.W. | title=On the random-cluster model | journal=Physica | publisher=Elsevier BV | volume=57 | issue=4 | year=1972 | issn=0031-8914 | doi=10.1016/0031-8914(72)90045-6 | pages=536–564| bibcode=1972Phy....57..536F }}
*{{cite journal | last1=Wang | first1=Jian-Sheng | last2=Swendsen | first2=Robert H. | title=Cluster Monte Carlo algorithms | journal=Physica A: Statistical Mechanics and Its Applications | publisher=Elsevier BV | volume=167 | issue=3 | year=1990 | issn=0378-4371 | doi=10.1016/0378-4371(90)90275-w | pages=565–579| bibcode=1990PhyA..167..565W }}
*{{cite journal | last=Barbu | first=A. | title=Generalizing Swendsen-Wang to sampling arbitrary posterior probabilities | journal=IEEE Transactions on Pattern Analysis and Machine Intelligence | publisher=Institute of Electrical and Electronics Engineers (IEEE) | volume=27 | issue=8 | year=2005 | issn=0162-8828 | doi=10.1109/tpami.2005.161 | pages=1239–1253| pmid=16119263 | bibcode=2005ITPAM..27.1239B | s2cid=410716 }}
{{DEFAULTSORT:Swendsen-Wang algorithm}}
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