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

摘要

We study the stochastic parallel dynamics of Ising spin systems defined onfinitely connected directed random graphs with arbitrary degree distributions,using generating functional analysis. For fully asymmetric graphs the dynamicsof 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 fewtime steps, and we construct approximate stationary solutions.