Damage spreading and coupling in spin glasses and hard spheres

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.

21 pages, 9 figures

References in corpus (14)

• Two-step melting in two dimensions: First-order liquid-hexatic transition
• A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
• The critical behavior of three-dimensional Ising spin glass models
• Critical parameters of the three-dimensional Ising spin glass
• Stiffness of the Edwards-Anderson Model in all Dimensions
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• The mixing time evolution of Glauber dynamics for the mean-field Ising model
• Exact Algorithm for Sampling the 2D Ising Spin Glass
• Renormalization group approach to exact sampling
• Damage spreading and coupling in Markov chains
• Sparse hard-disk packings and local Markov chains
• Lower Bounds on the Critical Density in the Hard Disk Model via Optimized Metrics
• Lower bound on the mean square displacement of particles in the hard disk model
• Convergence and coupling for spin glasses and hard spheres