Abstract
The authors construct the replica mean-field theory of a set of m-dimensional uniaxial quadrupoles interacting via quenched random exchange with non-zero mean. Replica-symmetric theory yields a transition which is continuous for m mc. For m>2 replica-symmetry breaking effects are much stronger than for conventional systems. Using the replica-symmetry breaking scheme of Parisi (1979), a solution is obtained but it appears to be unphysical for m>1/2(1+ square root 33) approximately=3.4. At sufficiently low temperatures, and for m>2, mean-field theory predicts that 'ferromagnetic' order is inevitable in the presence of disorder, regardless of the mean exchange.
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