Discussion
Despite its simplicity as a model of a physical system, the Potts model is useful as a model system for the study of phase transitions. For example, two dimensional lattices with exhibit a first order transition if . When a continuous transition is observed, as in the Ising model where . Further use is found through the model's relation to percolation problems and the Tutte and chromatic polynomials found in combinatorics.
The model has a close relation to the Fortuin-Kasteleyn random cluster model, another model in statistical mechanics. Understanding this relationship has helped develop efficient Markov chain Monte Carlo methods for numerical exploration of the model at small .
For integer values of q, the model displays the phenomenon of 'interfacial adsorption' with intriguing critical wetting properties when fixing opposite boundaries in two different states.
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