Facilitated kinetic Ising models and the glass transition

The class of ‘‘facilitated’’ kinetic Ising models introduced in a recent letter is investigated in greater detail. An interpretation of the models in terms of relaxation processes in dense fluids is described. Various types of kinetic behavior are predicted for the different spin models: (A) Arrhenius temperature dependence of the average structural relaxation time, (B) non-Arrhenius temperature dependence with a divergence of the relaxation time at a nonzero temperature, and (C) non-Arrhenius temperature dependence with a divergent relaxation time only at zero temperature. All of the models show nonexponential decay of equilibrium time correlation functions, consistent with the Kohlrausch–Williams–Watts empirical form. The nature of the glass transitions exhibited by the various models is discussed.