On Damage Spreading Transitions

TL;DR

This paper analyzes damage spreading transitions in one-dimensional stochastic cellular automata, revealing their connection to directed percolation and providing a phase diagram through mean field approximation.

Contribution

It introduces an original formalism for microscopic dynamics and extends the analysis to all symmetric cellular automata with two inputs, including the Ising model.

Findings

Damage spreading follows a directed percolation structure.

Phase diagram mapping from density to damage transition.

Applicable to symmetric cellular automata, including Ising model.

Abstract

We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able to show analitically that the evolution of the damage between two systems driven by the same noise has the same structure of a directed percolation problem. By means of a mean field approximation, we map the density phase transition into the damage phase transition, obtaining a reliable phase diagram. We extend this analysis to all symmetric cellular automata with two inputs, including the Ising model with heath-bath dynamics.