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The '''Swendsen–Wang algorithm''' is an [[algorithm]] for [[Monte Carlo simulation]] of the [[Ising model]] in which the entire sample is divided into equal-spin clusters. Each cluster is then assigned a new random spin value. Compare the [[Wolff algorithm]].
It is one of the first algorithms based on global changes to the system in a single sweep of moves. The original algorithm was designed for the Ising and Potts models, and later it was generalized to other systems as well, such as the XY model [[Wolff algorithm]] and particles of fluids. A key ingredient of the method is based on the representation of the Ising/Potts model through percolation models of connecting bonds due to Fortuin and Kasteleyn. These bonds form so-called clusters. Nearest sites of equal-spins are joined together by the bonds with a probability, P=1-exp(-2J/(k<sub>B</sub>T)), where J is the coupling constant for the ferromagnetic Ising model, T is temperature, and k<sub>B</sub> is Boltzmann constant. The clusters are then “flipped” together with equal probabilities. The method is most efficient near a second-order phase transition point, overcoming the critical slowing down.
It has been generalized by Barbu and Zhu (2005) to sampling arbitrary probabilities by viewing it as a [[Metropolis–Hastings algorithm]] and computing the acceptance probability of the proposed Monte Carlo move.
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