Potts model with invisible colors: random-cluster representation and Pirogov–Sinai analysis

Abstract

We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among q "visible" colors along with the presence of r non-interacting "invisible" colors. 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. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0129055X12500043