Dynamic mean-field and cavity methods for diluted Ising systems

Abstract

We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks the dynamic cavity method generally predicts magnetizations of individual spins better than both first order ("naive") and second order ("TAP") dynamic mean field theory.

References in corpus (6)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Stochastic Models of Evolution in Genetics, Ecology and Linguistics
• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Majority dynamics on trees and the dynamic cavity method
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• A message-passing scheme for non-equilibrium stationary states

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