A message-passing scheme for non-equilibrium stationary states

TL;DR

This paper applies the dynamic cavity method to analyze stationary states in a diluted asymmetric Ising model, comparing different update rules and demonstrating high accuracy and computational efficiency at high temperatures.

Contribution

It extends the dynamic cavity method to study non-equilibrium stationary states with different update schemes, highlighting its accuracy and limitations.

Findings

High accuracy of the dynamic cavity method at high temperatures.

Different behaviors for sequential and parallel updates at low temperatures.

Significant speed-up over Monte Carlo simulations when the method converges.

Abstract

We study stationary states in a diluted asymmetric (kinetic) Ising model. We apply the recently introduced dynamic cavity method to compute magnetizations of these stationary states. Depending on the update rule, different versions of the dynamic cavity method apply. We here study synchronous updates and random sequential updates, and compare local properties computed by the dynamic cavity method to numerical simulations. Using both types of updates, the dynamic cavity method is highly accurate at high enough temperatures. At low enough temperatures, for sequential updates the dynamic cavity method tends to a fixed point, but which does not agree with numerical simulations, while for parallel updates, the dynamic cavity method may display cyclic behavior. When it converges and is accurate, the dynamic cavity method offers a huge speed-up compared to Monte Carlo, particularly for large systems.