Potts model with invisible colours Random-cluster representation and Pirogov-Sinai analysis
نویسندگان
چکیده
We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among q “visible” colours along with the presence of r non-interacting “invisible” colours. We introduce a random-cluster representation for the model, for which we prove the existence of a first-order transition for any q > 0, as long as r is large enough. When q > 1, the low-temperature regime displays a q-fold symmetry breaking. The proof involves a Pirogov-Sinai analysis applied to this random-cluster representation of the model.
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