Random-anisotropy Blume-emery-griffiths Model

We describe the results of studies of a random-anisotropy Blume-Emery-Griffiths spin-1 Ising model using mean-field theory, transfer-matrix calculations, and position-space renormalization-group calculations. The interplay between the quenched randomness of the anisotropy and the annealed disorder introduced by the spin-1 model leads to a rich phase diagram with a variety of phase transitions and reentrant behavior. Our results may be relevant to the study of the phase separation of He-3-He-4 mixtures in porous media in the vicinity of the superfluid transition.