Monte carlo methods and glassy systems

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Abstract
The Monte Carlo method in statistical mechanics yields both equilibrium averages for model systems and information on relaxation processes described by master equations. It is a very useful tool for the study of short range spin glasses and orientational glasses. The numerical results for three—dimensional Ising and Potts glasses suggest an equilibrium phase transition to a glass phase at a nonzero freezing temperature, Tf>0. Freezing of isotropic spin and quadrupolar glasses is a nonequilibrium phenomenon, associated with a zero—temperature transition (Tf=0). All these systems are compatible with a Kohlrausch—type relaxation, i.e. the time—dependent Edwards—Anderson order parameter q(t) decays with time t as q(t)∼exp[—(t/τ)-y] for T>Tf. Since the relaxation time τ increases dramatically at low temperatures, it is very difficult to obtain accurate results on these models, and many open questions remain.

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