Potts model with invisible colours: 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" 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.

References in corpus (2)

• Phase Transition in Potts Model with Invisible States
• Phase Transition of Generalized Ferromagnetic Potts Model - Effect of Invisible States -

Cited by in corpus (7)

• Potts Model with Invisible States: A Review
• Potts Models with Invisible States on General Bethe Lattices
• Marginal dimensions of the Potts model with invisible states
• Potts Models with (17) Invisible States on Thin Graphs
• Ising model with invisible states on scale-free networks
• Potts model with invisible states on a scale-free network
• Changeover phenomenon in randomly colored Potts models