A Cluster Variation Method Approach to the Problem of Low-Temperature Statistics of a Class of Ising Models

Abstract

We Study the low-temperature thermodynamical and statistical properties of the ASYNNNI model, used to describe oxygen ordering in YBa₂Cu₃O_6+2c. Analyzing the excited states we show that this model undergoes a second order phase transition at absolute zero temperature. From the divergence of the relative energy fluctuations, in the limit T→0, we deduce that for T≈0 the deviation of the chemical potential μ from its ground state value is linearly related to the partial derivative of the fraction of threefold coordinated Cu(1) ions n with respect to oxygen concentlation c. We use the cluster variation method (CVM) to determine the numerical value of the coefficient of this relation and find that it is equal to −1⁄2, independently of the values of the interaction parameters. This establishes a full equivalence between the ASYNNNI model and the one-dimensional Ising model, where the role of the nearest-neighbor interaction of the latter is played by the V₂ interaction in the former. We comment on the general applicability of low levels of the CVM approximation to systems equivalent to the one-dimensional Ising model.