Metastability in stochastic dynamics of disordered mean-field models

Details Metastability in stochastic dynamics of disordered mean-field models Metastability in stochastic dynamics of disordered mean-field models

1998-11-24

arxiv.org/abs/cond-mat/9811331v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

73pp, AMSTEX

Scientific paper

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic sequence of ``admissible transitions''. For these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant. The distribution rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context of the random field Curie-Weiss model.

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