Isotropic Edwards-Anderson Models for Quadrupolar Glasses: A Monte Carlo Simulation

As a model for an orientational glass, we consider quadrupoles on a simple cubic lattice with random Gaussian bonds J ij . We treat the fully isotropic model described by the Hamiltonian, where S i is the μ-th component of a m -component vector (both m = 2 and m = 3 are treated) and the sum extends over all nearest-neighbour pairs once. Monte Carlo simulations show that the time-autocorrelation function of the quadrupoles is consistent with a stretched exponential form, and the relaxation time only diverges at zero temperature.