Cluster Variation Approach to the Random-Anisotropy Blume-Emery-Griffiths Model

TL;DR

This paper applies the cluster variation method to analyze the random-anisotropy Blume-Emery-Griffiths model, revealing complex phase behaviors and correlations that improve upon mean field predictions.

Contribution

It extends the cluster variation approach to disordered systems, uncovering new features like a rich ground state and a nonzero percolation threshold in the model.

Findings

Discovery of a rich ground state and a nonzero percolation threshold.

Identification of a reentrant coexistence curve and a high-concentration miscibility gap.

Nearest neighbor correlations raise the critical temperature and affect phase separation.

Abstract

The random--anisotropy Blume--Emery--Griffiths model, which has been proposed to describe the critical behavior of $^3$He--$^4$He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to disordered systems. Several new features, with respect to mean field theory, are found, including a rich ground state, a nonzero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high $^3$He concentration side down to zero temperature. Furthermore, nearest neighbor correlations are introduced in the random distribution of the anisotropy, which are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and contribute to the detachment of the coexistence curve from the $\lambda$ line.