A simple approach to the dynamics of Ising spin systems
(English)Manuscript (preprint) (Other academic)
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.
variational approximations, spin dynamics, Glauber dynamics, cluster variation method, path probability method
Research subject Physics
IdentifiersURN: urn:nbn:se:kth:diva-192098OAI: oai:DiVA.org:kth-192098DiVA: diva2:958022
QC 201609052016-09-052016-09-052016-09-05Bibliographically approved