A New Cluster Approximation to the Diluted Ising and Heisenberg Ferromagnets

Abstract

A new cluster approximation which enables us to describe both the diluted Ising and Heisenberg spin systems quantitatively is proposed. This approximation is based upon a cluster expansion formula for the magnetization and density matrices obtained by introducing stochastic variables. It is systematically improved by expanding the size of clusters to be considered. The 1-, 2- and 3-site approximations are applied to the diluted ferromagnets with the nearest-neighbor interaction. Concentration dependence on the Curie temperature for the Heisenberg model is quite different from that for the Ising model, while values of the critical concentration for these two models are almost the same. Dependence of the thermal average of a spin variable on its local environment is also studied.