Dynamical heterogeneity in the Ising spin glass

We investigate the relationship between bulk and local relaxation in the Ising spin glass (in two and three dimensions) for temperatures above but approaching the glass transition temperature, using Monte Carlo computer simulations. We find that the stretched exponential form of the bulk spin autocorrelation function results from a spatial average over a broad range of behavior, from strongly nonexponential to nearly exponential, for the local autocorrelation functions. The spatial correlation of single-site relaxation times obtained from these functions provides a length scale for dynamical heterogeneity that grows with decreasing temperature.