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)

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.