Monte Carlo investigation of a kinetic Ising model of the glass transition

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Abstract
A detailed Monte Carlo study of the equilibrium and dynamical properties of the two-spin facilitated kinetic Ising model proposed by Fredrickson and Andersen (FA) is presented. The model Hamiltonian is that of a spin-1/2 Ising model in an external magnetic field and, in the present study, contains no interactions between spins. The kinetic properties of the model are described by a master equation with single-spin-flip dynamics and highly cooperative flip rates. In particular, the rate at which a spin flips is chosen to be zero unless at least two of its neighbors are spin up. Monte Carlo simulations of the model on a square lattice demonstrate that although there is no evidence for a kinetic singularity (as predicted by FA), the model has dynamical properties much like those of viscous liquids. We find non-Arrhenius temperature dependence of the average relaxation time and highly nonexponential decay of various relaxation functions. The expression derived by Adam and Gibbs is found to describe the relationship between the average relaxation time and the entropy of the spin model. It is shown that the equilibrium time correlation functions can be accurately fit to the Kohlrausch–Williams–Watts (KWW) expression. The exponent in the KWW function is found to decrease as the temperature is lowered. Studies of multiple-spin correlation functions demonstrate how spatial correlations develop in the model as it is perturbed from equilibrium and how these relax as the system equilibrates.

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