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

Abstract

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 $\beta ⩾0$ and $h⩾0$, 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.

17 pages

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Cited by in corpus (5)

• Metastability for the degenerate Potts Model with negative external magnetic field under Glauber dynamics
• Yang-Lee zeros and the critical behavior of the infinite-range two- and three-state Potts models
• Metastability of the three-state Potts model with general interactions
• Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics
• Tunneling behavior of Ising and Potts models in the low-temperature regime