Renormalization Group Approach to Exact Sampling

2007/07/31 by Cedric Chanal, Cédric Chanal, Werner Krauth · 1 citation
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.100.060601

published as Physical Review Letters 100, 060601 (2008) · 4 pages, 4 figures (published version)

openalex publication_date 2008/02/15 · arxiv created 2008/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this Letter, we use a general renormalization-group algorithm to implement Propp and Wilson's "coupling from the past" approach to complex physical systems. Our algorithm follows the evolution of the entire configuration space under the Markov chain Monte Carlo dynamics from parts of the configurations (patches) on increasing length scales, and it allows us to generate "exact samples" of the Boltzmann distribution, which are rigorously proven to be uncorrelated with the initial condition. We validate our approach in the two-dimensional Ising spin glass on lattices of size 64 x 64.

Citations

• Exact sampling from nonattractive distributions using summary states

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• An eigenvalue method for computing the largest relaxation time of disordered systems

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