Renormalization group approach to exact sampling

TL;DR

This paper introduces a renormalization-group algorithm that enables exact, uncorrelated sampling from the Boltzmann distribution in complex physical systems, validated on a 2D Ising spin glass.

Contribution

It presents a novel renormalization-group method to implement exact sampling via coupling from the past for complex systems.

Findings

Successfully applied to 2D Ising spin glass

Generates uncorrelated exact samples

Validates the approach's effectiveness

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.