Relaxation of Random Magnets: Exact Results for the Griffiths' Regime

#### F. Cesi, C. Maes, F. Martinelli

1997, v.3, №4, 465-474

ABSTRACT

We study the relaxation to equilibrium for the kinetic Ising model with random many-body short range (not necessarily ferromagnetic) interactions in the Griffiths' regime. The speed of convergence for local observables to their thermal averages for typical realizations of the disorder is given by $\exp\{-t \exp\{-k (\log t)^\alpha\}\}$, where $\alpha = (d-1)/d$ in $d>1$ dimensions. When averaged over the disorder (or, when taking spatial averages) the decay is of the form $\exp\{-k(\log t)^{1/\alpha}\}$, in agreement with previous results obtained for the dilute Ising model.

Keywords: random spin systems,glassy dynamics,relaxation time,Griffiths' singularities,stretched exponential