First-order transition in Potts models with "invisible' states: Rigorous proofs
Statistical Mechanics
2011-12-03 v2 Mathematical Physics
math.MP
Probability
Abstract
In some recent papers by Tamura, Tanaka and Kawashima [arXiv:1102.5475, arXiv:1012.4254], a class of Potts models with "invisible" states was introduced, for which the authors argued by numerical arguments and by a mean-field analysis that a first-order transition occurs. Here we show that the existence of this first-order transition can be proven rigorously, by relatively minor adaptations of existing proofs for ordinary Potts models. In our argument we present a random-cluster representation for the model, which might be of independent interest.
Cite
@article{arxiv.1106.5907,
title = {First-order transition in Potts models with "invisible' states: Rigorous proofs},
author = {Aernout C. D. van Enter and Giulio Iacobelli and Siamak Taati},
journal= {arXiv preprint arXiv:1106.5907},
year = {2011}
}