Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions

Details Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions

2009-07-10

arxiv.org/abs/0907.1699v2

J. Phys. A: Math. Theor., 42, 415001 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages, 4 figures

Scientific paper

10.1088/1751-8113/42/41/415001

We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the system can be completely solved, due to the asymptotic absence of loops. For arbitrary graph symmetry, we solve the dynamics exactly for the first few time steps, and we construct approximate stationary solutions.

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