Damage spreading and dynamic stability of kinetic Ising models

TL;DR

This paper studies how initial conditions influence the evolution of kinetic Ising models, identifying regular and chaotic phases through a master equation approach and stability analysis.

Contribution

It introduces a master equation for the joint evolution of two identical kinetic Ising systems under the same noise, revealing phases of regular and chaotic behavior.

Findings

Identification of regular and chaotic phases in kinetic Ising models

Derivation of a master equation for joint probability evolution

Analysis of fixed points and their stability

Abstract

We investigate how the time evolution of different kinetic Ising models depends on the initial conditions of the dynamics. To this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise. We derive a master equation for the time evolution of a joint probability distribution of the two systems. This equation is then solved within an effective-field approach. By analyzing the fixed points of the master equation and their stability we identify regular and chaotic phases.