Replica theory of the uniaxial quadrupolar glass

We 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 < m_c = 4.6 but discontinuous m> m_c. For m> 2 replica-symmetry breaking effects are much stronger than for conventional systems. Using the replica-symmetry breaking scheme of Parisi, a solution is obtained but it appears to be unphysical for m>1/2(1 + V33) = 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.