In an Ising model with spin-exchange dynamics damage always spreads

TL;DR

This paper studies damage spreading in Ising models with Kawasaki spin-exchange dynamics, showing that damage always propagates and never heals, contrasting with other dynamics, confirmed by theoretical and simulation results.

Contribution

It develops an effective-field theory for damage spreading in Ising models with Kawasaki dynamics, extending previous approaches to more complex spin-exchange rules.

Findings

Damage always spreads in Kawasaki dynamics.

Long-time damage approaches uncorrelated systems.

Monte-Carlo simulations confirm theoretical predictions.

Abstract

We investigate the spreading of damage in Ising models with Kawasaki spin-exchange dynamics which conserves the magnetization. We first modify a recent master equation approach to account for dynamic rules involving more than a single site. We then derive an effective-field theory for damage spreading in Ising models with Kawasaki spin-exchange dynamics and solve it for a two-dimensional model on a honeycomb lattice. In contrast to the cases of Glauber or heat-bath dynamics, we find that the damage always spreads and never heals. In the long-time limit the average Hamming distance approaches that of two uncorrelated systems. These results are verified by Monte-Carlo simulations.