Monte Carlo study of the Potts glass with nearest-neighbour random Gaussian interaction

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Abstract
The three-state Potts model with nearest-neighbour random Gaussian interaction on the simple cubic lattice is investigated by Monte Carlo simulation. Both static quantities (e.g. glass ordering susceptibility and the correlation function) and dynamic quantities (the analogue of the time-dependent Edwards-Anderson order parameter q(t) for Potts spins) are obtained. As for related models for orientational glasses, it is found that q(t) is consistent with the Kohlrausch law q(t) varies as exp(-(t/ tau )y) for a wide range of temperatures, with a strongly temperature-dependent exponent y, with y becoming very small as the temperature T to 0. The relaxation time tau increases dramatically as T is lowered; thus the system could only be equilibrated for temperatures where the correlation length is rather small. Since the critical region has not been reached, it cannot be distinguished whether the critical temperature Tc is non-zero or at T=0. If Tc=0, the divergences of tau and the ordering susceptibility are probably exponential, i.e. the system is then at its lower critical dimensionality.

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