Damage spreading and coupling in spin glasses and hard spheres

TL;DR

This paper explores the relationship between damage spreading and Markov chain coupling in disordered systems like spin glasses and hard spheres, providing insights into phase transitions and mixing times.

Contribution

It establishes a connection between damage spreading and coupling techniques, analyzing their implications for phase behavior in disordered systems.

Findings

Scaling analysis identifies a critical point between fast and slow coupling regimes.

Coupling insights shed light on phase transitions in spin glasses and hard spheres.

Numerical results suggest a link between rapid coupling and disordered phases.

Abstract

We study the connection between damage spreading, a phenomenon long discussed in the physics literature, and the coupling of Markov chains, a technique used to bound the mixing time. We discuss in parallel the Edwards-Anderson spin glass model and the hard-disk system, focusing on how coupling provides insights into the region of fast coupling within the paramagnetic and liquid phases. We also work out the connection between path coupling and damage spreading. Numerically, the scaling analysis of the mean coupling time determines a critical point between fast and slow couplings. The exact relationship between fast coupling and disordered phases has not been established rigorously, but we suggest that it will ultimately enhance our understanding of phase behavior in disordered systems.