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We study the Glauber dynamics of Ising spin models with random bonds, onfinitely connected random graphs. We generalize a recent dynamical replicatheory with which to predict the evolution of the joint spin-fielddistribution, to include random graphs with arbitrary degree distributions. Thetheory is applied to Ising ferromagnets on randomly diluted Bethe lattices,where we study the evolution of the magnetization and the internal energy. Itpredicts a prominent slowing down of the flow in the Griffiths phase, itsuggests a further dynamical transition at lower temperatures within theGriffiths phase, and it is verified quantitatively by the results of MonteCarlo simulations.

Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet