Theory of orientational glasses models, concepts, simulations

Abstract This review describes the various attempts to develop a theoretical understanding for ordering and dynamics of randomly diluted molecular crystals, where quadrupole moments freeze in random orientations upon lowering the temperature, as a result of randomness and competing interactions. While some theories attempt to model this freezing into a phase with randomly oriented quadrupole moments in terms of a bond-disorder concept analogous to the Edwards-Anderson model of spin glasses, other theories attribute the freezing to random field-like terms in the Hamiltonian. While models of the latter type have been studied primarily by microscopic molecular field-type treatments, the former models have been treated both in the Sherrington-Kirkpatrick-Parisi infinite-range limit, and in the short-range case. Among the surprising findings of these treatments we emphasize the first-order glass transition (though lacking a latent heat) of the infinite-range Potts glass, the suggestion that the short-range Potts glass in d = 3 is at its lower critical dimension, and the fact that Potts glasses at zero temperature have a non-zero entropy even for continuous distribution of the interactions. Combining the theoretical results with pertinent experimental findings, it is shown that no definite conclusions on what is the best model for orientational glasses can as yet be drawn, and probably the different classes of models should rather be considered as simple limiting cases of a very complex behaviour.