A simple approach to the dynamics of Ising spin systems

We study a novel variational approach to solve the dynamics of Ising-like discrete spin systems. The equations are derived under mean-field approximations based on the cluster variational method. Comparison with the actual Glauber dynamics of models defined on Erdos-R\'enyi random graphs show that some of these approximations are extremely accurate, both at equilibrium and in the off-equilibrium regime, providing the same result of the Monte Carlo simulation in a much shorter time. The models studied are the ferromagnetic kinetic Ising model (both with symmetric and partially asymmetric interactions), the random field Ising model and the Viana-Bray model. Only for the latter model we find some small discrepancies in the very low temperature phase, probably due to the existence of a large number of metastable states.QC 20160905