Models of cooperative diffusion

Abstract

According to the results presented above, our two models of cooperative dynamics — the lattice gas on the triangular lattice with two-vacancy assisted hopping and the asymmetric one-spin facilitated kinetic Ising model — have the common characteristic of a very rapid slowing down of particle or spin motion as a function of the control parameter. For the lattice gas model, Monte Carlo results — contrary to the result of an analytical pair approximation — led us to expect the self-diffusion coefficient D _s to vanish faster than any positive power of the vacancy concentration (1 - c) for particle concentration c going to 1. For the spin model, the results of analytical and numerical calculations led us to conjecture that the spin autocorrelation function for finite chains decays exponentially for up-spin concentration c going to zero, from which a faster-than-power-law divergence of the mean spin relaxation time τ_∞ on infinite chains can be deduced. These results contrast with power laws obtained both by analytical calculation and Monte Carlo simulation for variants of the models with weaker kinetic constraints. These variants of our models may be interpreted as types of defect-diffusion models. Apparently, the absence of freely diffusing “defects” (vacancies or up spins) or defect complexes in our models of cooperative dynamics goes together with the very rapid slowing down, which qualitatively resembles the slowing down of diffusive motions in glass-forming liquids cooled towards their glass-transition temperatures.