The cooperativity length in models for the glass transition

Abstract

Kinetic Ising and lattice-gas models with kinetic constraints may serve as models of cooperative dynamics in undercooled liquids near the glass transition. For a class of these models the cooperativity length of a spin/particle is defined and its distribution calculated. It is found that, contrary to an assumption of Adam and Gibbs (1964), there is no simple relation between the cooperativity length and the entropy of these models. For the autocorrelation functions, which exhibit a stretched-exponential time dependence, an approximate sum formula is proposed which contains a relaxation rate depending on cooperativity length. The sum formula is tested for a particular case and found to give good overall agreement with Monte Carlo data.