Damage spreading and coupling in Markov chains

TL;DR

This paper explores the relationship between coupling of Markov chains and damage spreading, revealing that damage spreading limits perfect sampling in spin glasses and hard spheres, with transitions depending on coupling schemes.

Contribution

It demonstrates that damage spreading, not the configuration space survey, hinders perfect sampling, and shows how coupling schemes influence damage spreading transitions.

Findings

Damage spreading occurs inside paramagnetic and liquid phases.

Critical temperatures and densities depend on coupling schemes.

Non-Markovian coupling schemes can prevent damage spreading.

Abstract

In this paper, we relate the coupling of Markov chains, at the basis of perfect sampling methods, with damage spreading, which captures the chaotic nature of stochastic dynamics. For two-dimensional spin glasses and hard spheres we point out that the obstacle to the application of perfect-sampling schemes is posed by damage spreading rather than by the survey problem of the entire configuration space. We find dynamical damage-spreading transitions deeply inside the paramagnetic and liquid phases, and show that critical values of the transition temperatures and densities depend on the coupling scheme. We discuss our findings in the light of a classic proof that for arbitrary Monte Carlo algorithms damage spreading can be avoided through non-Markovian coupling schemes.