 96258 Filippo Cesi, Christian Maes and Fabio Martinelli
 Relaxation to equilibrium for two dimensional
disordered Ising systems in the Griffiths phase
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Jun 12, 96

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Abstract. We consider Glaubertype dynamics for two dimensional disordered
magnets of Ising type. We prove that, if in equilibrium
the disorderaveraged influence of the
boundary condition is sufficiently small, then the corresponding
Glauber dynamics is ergodic with probability one and the disorderaveraged of
timeautocorrelations 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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