Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model

The Curie-Weiss-Potts model, a model in statistical mechanics, is parametrized by the inverse temperature [beta] and the external magnetic field h. This paper studies the asymptotic behavior of the maximum likelihood estimator of the parameter [beta] when h = 0 and the asymptotic behavior of the maximum likelihood estimator of the parameter h when [beta] is known and the true value of h is 0. The limits of these maximum likelihood estimators reflect the phase transition in the model; i.e., different limits depending on whether [beta] < [beta]c, [beta] = [beta]c or [beta] > [beta]c, where [beta]c [epsilon] (0, [infinity]) is the critical inverse temperature of the model.