Limit Theorems and Coexistence Probabilities for the Curie-Weiss Potts Model with an external field

Details Limit Theorems and Coexistence Probabilities for the Curie-Weiss Potts Model with an external field Limit Theorems and Coexistence Probabilities for the Curie-Weiss Potts Model with an external field

2008-11-17

arxiv.org/abs/0811.2735v1

Stochastic Processes and their Applications 120 (2010) 84-104

Mathematics

Probability

17 pages

Scientific paper

10.1016/j.spa.2009.10.011

The Curie-Weiss Potts model is a mean field version of the well-known Potts model. In this model, the critical line $\beta = \beta_c (h)$ is explicitly known and corresponds to a first order transition when $q > 2$. In the present paper we describe the fluctuations of the density vector in the whole domain $\beta \geqslant 0$ and $h \geqslant 0$, including the conditional fluctuations on the critical line and the non-Gaussian fluctuations at the extremity of the critical line. The probabilities of each of the two thermodynamically stable states on the critical line are also computed. Similar results are inferred for the Random-Cluster model on the complete graph.

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