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arXiv · 1109.0189

Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis

Aernout C. D. van Enter·Giulio Iacobelli·Siamak Taati
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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.

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Aernout C. D. van Enter, Giulio Iacobelli, Siamak Taati. 2011-09-01. Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis. https://doi.org/10.1142/s0129055x12500043

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