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

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.

14 pages (plain TeX) + 12 figures (PostScript, appended), Preprint POLFIS-TH.02/93

Cited by in corpus (11)

• Real-Space Renormalization Group Study of the Two-dimensional Blume-Capel Model with a Random Crystal Field
• Study of the mixed Ising spins (1/2,3/2) in a random crystal field
• Critical behavior and phase diagrams of a spin-1 Blume-Capel model with random crystal field interactions: An effective field theory analysis
• Mean field solution of the Blume-Capel model under a random crystal field
• Monte Carlo study of the two-dimensional kinetic Blume-Capel model in a quenched random crystal field
• Emergence of a bicritical end point in the random crystal field Blume-Capel model
• Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field
• Monte Carlo studies of the Blume-Capel model on nonregular two- and three-dimensional lattices: Phase diagrams, tricriticality, and critical exponents
• Folding of the Triangular Lattice with Quenched Random Bending Rigidity
• Absence of first order transition in the random crystal field Blume-Capel model on a fully connected graph
• Hysteresis behaviours of the crystal field diluted general spin-S Ising model