Limit theorems and coexistence probabilities for the Curie-Weiss Potts model with an external field

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. (C) 2009 Published by Elsevier B.V.