Stochastic dynamics of coupled systems and spreading of damage

TL;DR

This paper investigates how damage propagates in a one-dimensional Ising model using stochastic dynamics, mapping it to a probabilistic cellular automaton, and identifies the critical conditions for damage spreading through simulations and mean-field analysis.

Contribution

It introduces a novel approach by coupling the Ising model with its replica via algorithms interpolating between heat bath and Hinrichsen-Domany methods, and maps the dynamics to a cellular automaton.

Findings

Identified the critical line for damage spreading.

Mapped the high-temperature dynamics to a probabilistic cellular automaton.

Used mean-field and Monte Carlo methods to analyze phase transition.

Abstract

We study the spreading of damage in the one-dimensional Ising model by means of the stochastic dynamics resulting from coupling the system and its replica by a family of algorithms that interpolate between the heat bath and the Hinrichsen-Domany algorithms. At high temperatures the dynamics is exactly mapped into de Domany-Kinzel probabilistic cellular automaton. Using a mean-field approximation and Monte Carlo simulations we find the critical line that separates the phase where the damage spreads and the one where it does not.