Distributional Approximation for General Curie–Weiss Models with Size-dependent Inverse Temperatures

The Curie–Weiss model is a statistical physics model that describes the behavior of a system of particles with mutual interactions. In this paper, we apply Stein’s method to establish Berry–Esseen bounds for both normal and non-normal approximations of a broad types of Curie–Weiss model, incorporating a size-dependent inverse temperature. Our result encompasses the Blumer-Emery-Griffiths model as a particular instance, while surpassing the convergence rate of earlier findings by Eichelsbacher and Martschink (2014). By using Stein’s method, we provide a comprehensive analysis of the Curie–Weiss model, offering improved bounds on the rate of convergence.