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The random--anisotropy Blume--Emery--Griffiths model, which has been proposedto describe the critical behavior of $^3$He--$^4$He mixtures in a porousmedium, is studied in the pair approximation of the cluster variation methodextended to disordered systems. Several new features, with respect to meanfield theory, are found, including a rich ground state, a nonzero percolationthreshold, a reentrant coexistence curve and a miscibility gap on the high$^3$He concentration side down to zero temperature. Furthermore, nearestneighbor correlations are introduced in the random distribution of theanisotropy, which are shown to be responsible for the raising of the criticaltemperature with respect to the pure and uncorrelated random cases andcontribute to the detachment of the coexistence curve from the $\lambda$ line.Comment: 14 pages (plain TeX) + 12 figures (PostScript, appended), Preprint  POLFIS-TH.02/9

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