Parallel dynamics of disordered Ising spin systems on finitely connected random graphs

Details Parallel dynamics of disordered Ising spin systems on finitely connected random graphs Parallel dynamics of disordered Ising spin systems on finitely connected random graphs

2004-03-05

arxiv.org/abs/cond-mat/0403172v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

LaTeX, 10 eps figures, submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/37/24/001

We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems), the dynamic order parameter is here a measure which represents the disorder averaged single-spin path probabilities, given external perturbation field paths. In the limit of completely asymmetric graphs our macroscopic laws close already in terms of the single-spin path probabilities at zero external field. For the general case of arbitrary graph symmetry we calculate the first few time steps of the dynamics exactly, and we work out (numerical and analytical) procedures for constructing approximate stationary solutions of our equations. Simulation results support our theoretical predictions.

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