Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2009-01-07
Physics
Condensed Matter
Disordered Systems and Neural Networks
30 pages, 4 figures, submitted to J.Phys.A
Scientific paper
We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations.
Coolen Anthony C. C.
Mozeika Alexander
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