A generalization of the usual spherical model of spin-glasses is introduced, and its static and dynamic behavior is fully studied. The generalized model is given the name quantum spherical model to contrast it with the usual model which we call the classical spherical model. The results of the quantum model reduce to those of the classical model in appropriate limits. However, the quantum model shows some new and interesting features. The equilibrium entropy of spin-glasses which is negative at sufficiently low temperatures in the classical model is found positive in the quantum version, and it vanishes at zero temperature. The dynamic properties of quantum and classical spherical models are similar except in the infinite time limit when different equilibrium behavior is obtained as expected. The magnetization, order-parameter, and on-site correlations are found to decay exponentially above the transition temperature, and algebraically at and below it in the long-time limit. A closed-form expression for the dynamic susceptibility valid at all temperatures is also obtained. The algebraic decay predicted by our model may serve as a model form of behavior in the interpretation of experimental relaxation data on spin-glasses.

• Received 22 December 1980

DOI:https://doi.org/10.1103/PhysRevB.23.4661