From Werner KRAUTH

C. Chanal, W. Krauth Renormalization group approach to exact sampling Physical Review Letters 100 060601 (2008)

Contents 1 Paper 2 Context 3 Algorithm

Paper

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.

Electronic version (from arXiv)

Original paper in Physical Review Letters (requires subscription)

Context

As shown in Bernard_Chanal_Krauth_2010, a transition from regular to chaotic dynamics taking place in the Monte Carlo algorithm is responsible for the breakdown of the algorithm at low temperatures.

Algorithm

A Python version of the algorithm developed in this paper was was presented in the 2010 follow-up paper