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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. A key ingredient is the 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 (2005) to
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