98-202 K. S. Alexander, Filippo Cesi, Lincoln Chayes,, Christian Maes and Fabio Martinelli

Convergence to Equilibrium of Random Ising Models in the Griffiths' Phase (233K, PS) Mar 16, 98

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Abstract. We consider Glauber--type dynamics for disordered Ising spin systems with nearest neighbor pair interactions in the Griffiths' phase. We prove that in a nontrivial portion of the Griffiths' phase the system has exponentially decaying correlations of distant functions with probability exponentially close to 1. This condition has, in turn, been shown \ref[CMM1] to imply that the convergence to equilibrium is faster than any stretched exponential, and that the {\it 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.

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