Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-12-07
Physics
Condensed Matter
Disordered Systems and Neural Networks
26 pages LaTeX, 5 figures
Scientific paper
10.1088/1751-8113/41/11/115003
We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-field probability distribution, and solve these within the replica symmetry ansatz. Although the theory is developed in a general setting, with a view to future applications in various other fields, in this paper we apply it mainly to the dynamics of the Glauber algorithm (extended with cooling schedules) when running on the so-called vertex cover optimization problem. Our theoretical predictions are tested against both Monte Carlo simulations and known results from equilibrium studies. In contrast to previous dynamical analyses based on deriving closed equations for only a small numbers of scalar order parameters, the agreement between theory and experiment in the present study is nearly perfect.
Coolen Anthony C. C.
Mozeika Alexander
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