Nonextensive entropy and the non-Gaussian distribution of magnetization in two-dimensional spin ice

The statistical properties of the magnetization of the finite clusters of two-dimensional spin ice have been investigated. It has been shown by Monte Carlo simulations that the short-range ice rules in two dimensions lead to long-range correlations, which decay by a power law with distance. The long-range correlations, in turn, cause the nonextensivity of entropy and inapplicability of the central limit theorem for the magnetization. The behavior of the moments and distribution function of the magnetization with the cluster size disagrees with the theoretical predictions of the dipolar behavior of the correlation functions in two-dimensional spin ice.