The ferromagnetic Potts model on a finite graph assigns possible states to each graph vertex and rewards neighbouring equal states by the displayed weight, for . The interaction sum counts each unoriented edge once. The Edwards-Sokal coupling identifies its spin clusters with the random-cluster model at and integer .
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The Potts model is a mathematical model used in statistical mechanics, particularly in the study of phase transitions in materials and systems. It is a generalization of the Ising model, which describes the behavior of magnetic spins. The Potts model extends the Ising model by allowing each lattice site to have more than two possible states.