Dynamic mean-field and cavity methods for diluted Ising systems

TL;DR

This paper compares dynamic mean-field and cavity methods for dilute kinetic Ising models, showing the cavity method's superior accuracy in predicting individual spin magnetizations.

Contribution

It introduces a comparison between dynamic mean-field and cavity methods, highlighting the cavity method's improved predictions for dilute networks.

Findings

Dynamic cavity method outperforms mean-field theories in dilute networks.

Third-order expansion in interaction strength improves mean-field accuracy.

Cavity method provides better individual spin magnetization estimates.

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.