Blume-Emery-Griffiths model in a random crystal field

We study the Blume-Emery-Griffiths model in a random crystal field in two a nd three dimensions, through a real-space renormalization-group approach an d a mean-field approximation, respectively. According to the two-dimensiona l renormalization-group calculation, non-symmetry-breaking first-order phas e transitions are eliminated and symmetry-breaking discontinuous transition s' are replaced by continuous ones, when disorder is introduced. On the oth er hand, the mean-field calculation predicts that first-order transitions a re not eliminated by disorder, although some changes are introduced in the phase diagrams. We make some comments on the consequences of a degeneracy p arameter, which may be relevant in martensitic transitions. [S0163-1829(99) 09925-7].