A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

The random-anisotropy Blume-Emery-Griffiths model, which has been proposed to describe the critical behaviour of ³He-⁴He 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 non-zero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high-³He-concentration side down to zero temperature. Furthermore, nearest-neighbour correlations are introduced into the random distribution of the anisotropy, and are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and to contribute to the detachment of the coexistence curve from the lambda line.