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 β and the external magnetic field h. This paper studies the asymptotic behavior of the maximum likelihood estimator of the parameter β when h = 0 and the asymptotic behavior of the maximum likelihood estimator of the parameter h when β 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 β < β_c, β = β_c or β > β_c, where β_c ε (0, ∞) is the critical inverse temperature of the model.