MEAN-FIELD STUDY OF THE DEGENERATE BLUME-EMERY-GRIFFITHS MODEL IN A RANDOM CRYSTAL-FIELD

The degenerate Blume-Emery-Griffiths (DBEG) model has recently been in troduced in the study of martensitic transformation problems. This mod el has the same Hamiltonian as the standard Blume-Emery-Griffiths (BEG ) model but, to take into account vibrational effects on the martensit ic transition, it is assumed that the states S = 0 have a degeneracy p (p = 1 corresponds to the usual BEG model). This model was studied by E. Vives et al. for a particular value of Delta, through a mean-field approximation and numerical simulation. When the parameter p increase s, the ferromagnetic phase shrinks and the region where the transition is of first order increases. In some materials, however, the transiti on would be better described by a disordered DBEG model; further, the inclusion of disorder in the DBEG model may be relevant in the study o f shape memory alloys. From the theoretical point of view, it would be interesting to study the consequence of conflicting effects: the para meter p, which increases the first-order phase-transition region, and disorder in the crystal field, which tends to diminish this region in three dimensions. In order to study this competition in high-dimension al systems, we apply a mean-held approximation: it is then possible to determine the critical behavior of the random DBEG model for any valu e of the interaction parameters. Finally, we comment on (preliminary) results obtained for a two-dimensional system, where the randomness in the crystal field has a more drastic effect, when compared to the thr ee-dimensional model. (C) 1998 Elsevier Science B.V. All nights reserv ed.