96-258 Filippo Cesi, Christian Maes and Fabio Martinelli

Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase (53K, TeX) Jun 12, 96

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Abstract. We consider Glauber--type dynamics for two dimensional disordered magnets of Ising type. We prove that, if in equilibrium the disorder--averaged influence of the boundary condition is sufficiently small, then the corresponding Glauber dynamics is ergodic with probability one and the disorder--averaged of time--autocorrelations decays like $\nep{-m (\log t)^{2}}$. For the standard dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values $0$ or $J>0$, our results apply even if the active bonds percolate and $J$ is larger than the critical value for the corresponding pure Ising model. For this model we also rigorously prove the existence of a dynamical phase transition when $J$ crosses the critical value $J_c$ for the standard two dimensional Ising model.

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