Parallel dynamics of disordered Ising spin systems on random graphs

摘要

We examine the non-equilibrium dynamics of bond-disordered Ising spin systems on random graphs with arbitrary degree distribution, using generating functional techniques. The dynamic order parameter is a measure describing the likelihood of a spin path, given a path of perturbations or external fields, which has a clear physical interpretation. For short times the order parameter set can be calculated exactly, while for longer times this is not possible and approximation schemes must be devised to study the dynamics. We study one such scheme and compare our results with simulations.