Analytic expressions for estimation of the critical properties of inhomogeneous Ising models

Abstract

In many applications of spin models, the fast estimation of their critical temperatures and other physical properties is of great importance. In this work, we present the analytical expressions estimating the critical properties of inhomogeneous Ising models with ferromagnetic interactions. The expressions were obtained within the framework of the m-vicinity method. The accuracy of the critical temperature estimations was evaluated through comparison with Monte Carlo simulations. Special attention was given to the case when the model consists of two interacting interpenetrating homogeneous sublattices, and relationships for the compositional dependence of the critical temperature were derived.