Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis
Mathematical Physics
2015-05-30 v1 Statistical Mechanics
math.MP
Probability
Abstract
We study a variant of the ferromagnetic Potts model, recently introduced by Tamura, Tanaka and Kawashima, consisting of a ferromagnetic interaction among "visible" colours along with the presence of 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 , as long as is large enough. When , the low-temperature regime displays a -fold symmetry breaking. The proof involves a Pirogov-Sinai analysis applied to this random-cluster representation of the model.
Keywords
Cite
@article{arxiv.1109.0189,
title = {Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis},
author = {Aernout C. D. van Enter and Giulio Iacobelli and Siamak Taati},
journal= {arXiv preprint arXiv:1109.0189},
year = {2015}
}