MONTE-CARLO METHODS AND GLASSY SYSTEMS

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 king 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). Al l 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 )$4exp[ - ( t /$$)y] for T>Tf. Since the relaxation time T increases dramatically at low temperatures, it is very difficult to obtain accurate results on these models, and many open questions remain. © 1990, Taylor & Francis Group, LLC. All rights reserved.