On rates of convergence in the Curie-Weiss-Potts model with external field

Abstract

In the present paper we obtain rates of convergence for the limit theorems of the density vector in the Curie-Weiss-Potts model via Stein's Method of exchangeable pairs. Our results include Kolmogorov bounds for multivariate normal approximation in the whole domain $β\geq 0$ and $h\geq 0$, where $β$ is the inverse temperature and $h$ an exterior field. In this model, the critical line $β= β_c(h)$ is explicitly known and corresponds to a first order transition. We include rates of convergence for non-Gaussian approximations at the extremity of the critical line of the model.