Cluster Variation Method Applications to Large Ising Aggregates

Abstract

The magnetic properties of very large Ising aggregates with various shapes are studied using the pair, triangle and square approximations of the Cluster Variation Method (CVM). To derive analytic expressions for the Curie temperature of clusters with an arbitrary number of sites we assume that the probability distributions do not depend on the position of the spins. Our results indicate that for very large clusters the critical temperature depends more on the geometrical characteristics (number of sites, number of pairs, number of planes, etc.) than on the position dependence of the cluster probabilities. We found that for a fixed number of atoms, the highest critical temperature corresponds to the more spherical aggregates. We compare our results with Monte Carlo simulations and with other CVM calculations in which the position dependence of the pair probabilities were taken into account. In the case of the high order approximations (triangle and square), we found that for aggregates with a number of atoms smaller than n*, the phase transition disappears. The number n* depends on the geometrical characteristics of the system.