96-299 Filippo Cesi, Christian Maes and Fabio Martinelli

Relaxation of Disordered Magnets in the Griffiths' Regime (126K, TeX) Jun 17, 96

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Abstract. We study the relaxation to equilibrium of discrete spin systems with random many--body (not necessarily ferromagnetic) interactions in the Griffiths' regime. We prove that the speed of convergence to the unique reversible Gibbs measure is almost surely faster than any stretched exponential, at least if the probability distribution of the interaction decays faster than exponential (e.g. Gaussian). Furthermore, if the interaction is uniformly bounded, the {\it average over the disorder\/} of the time--autocorrelation function, goes to equilibrium as $\exp[- k (\log t)^{d/(d-1)}]$ (in $d>1$), in agreement with previous results obtained for the dilute Ising model.

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