Damage spreading and coupling in Markov chains

Laboratoire de Physique Statistique, CNRS, UPMC, Ecole Normale Supérieure - 24 rue Lhomond, 75231 Paris Cedex 05, France, EU

^a etienne.bernard@ens.fr
^b werner.krauth@ens.fr

Received: 8 October 2010
Accepted: 2 December 2010

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 we show that the 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.