Filippo Cesi, Christian Maes and Fabio Martinelli
Relaxation of Disordered Magnets in the Griffiths' Regime
(126K, TeX)

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.