BLUME-EMERY-GRIFFITHS MODEL ON 3-DIMENSIONAL LATTICES - CONSEQUENCES FOR THE ANTIFERROMAGNETIC POTTS-MODEL

Using the cluster-variation method we study the phase diagram of the B lume-Emery-Griffiths (BEG) model on simple-cubic and face-centered cub ic lattices. For the simple-cubic lattice the main attention is paid t o reentrant phenomena and ferrimagnetic phases occurring in a certain range of coupling constants. The results are in close agreement with M onte Carlo data, available for parts of the phase diagram. Several fer rimagnetic phases are obtained in the vicinity of the line in paramete r space, at which the model reduces to the antiferromagnetic three-sta te Potts model. Our results imply the existence of three phase transit ions in the antiferromagnetic Potts model on the simple-cubic lattice. The phase diagrams for the BEG model on the face-centered cubic latti ce are obtained in the region of antiquadrupolar ordering. Also the se veral ordered phases of the antiferromagnetic Potts model on this latt ice are discussed.