CONVERGENCE TO EQUILIBRIUM OF RANDOM ISING-MODELS IN THE GRIFFITHS PHASE

We consider Glauber-type dynamics for disordered Ising spin systems wi th nearest neighbor pair interactions in the Griffiths phase. We prove that in a nontrivial portion of the Griffiths phase the system has ex ponentially decaying correlations of distant functions with probabilit y exponentially close to 1. This condition has, in turn, been shown el sewhere to imply that the convergence to equilibrium is faster than an y stretched exponential, and that the average over the disorder of the time-autocorrelation function goes to equilibrium faster than exp[-k( log t)(d/(d-1))]. We then show that for the diluted Ising model these upper bounds are optimal.