Dynamic message-passing approach for kinetic spin models with reversible dynamics
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, no 1, 010102Article in journal (Refereed) Published
A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally treelike topology is presented. The method builds on (a) a graph expansion to eliminate loops from the normalizations of each step in the dynamics and (b) an assumption that a set of auxilary probability distributions on histories of pairs of spins mainly have dependencies that are local in time. The closure is then effectuated by projecting these probability distributions on n-step Markov processes. The method is shown in detail on the level of ordinary Markov processes (n = 1) and outlined for higher-order approximations (n > 1). Numerical validations of the technique are provided for the reconstruction of the transient and equilibrium dynamics of the kinetic Ising model on a random graph with arbitrary connectivity symmetry.
Place, publisher, year, edition, pages
American physical society , 2015. Vol. 92, no 1, 010102
Fusion, Plasma and Space Physics
IdentifiersURN: urn:nbn:se:kth:diva-172162DOI: 10.1103/PhysRevE.92.010102ISI: 000358259400001OAI: oai:DiVA.org:kth-172162DiVA: diva2:846780
QC 201508182015-08-182015-08-142016-09-05Bibliographically approved