Simulation of Models for Isotropic and Anisotropic Orientational Glasses

Abstract

“Orientational glass” behavior is found when molecular crystals are randomly diluted, and quadrupole moments get frozen by random alignment of the molecules, similar to “spin glass” behavior of randomly diluted magnets. Monte Carlo simulation of lattice models where quadrupole moments interact with nearest neighbor Gaussian coupling is a unique tool to study this behavior. The time-dependent glass order parameter exhibits anomalously slow relaxation, compatible with the Kohlrausch-Williams-Watts (KWW) stretched exponential function. Both isotropic and anisotropic models exhibit in d=2 and d=3 spatial dimensions glass transitions at zero temperature only. While the glass correlation length and glass susceptibility in the isotropic case exhibit power law divergences as T→0, exponential divergences are found for the p=3-state Potts glass in d=3, suggesting that the latter system is at its lower critical dimension.