2000/05/08 by Andrew M. Childs, R. B. Patterson, Ryan B. Patterson +2
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics #cond-mat.stat-mech #math.PR
paper · pdf · doi:10.1103/physreve.63.036113
published as Phys. Rev. E 63, 036113 (2001) · 5 pages, 6 EPS figures, REVTeX; additional information at http://wol.ra.phy.cam.ac.uk/mackay/exact
arxiv created 2000/05/08 · openalex publication_date 2001/02/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Propp and Wilson's method of coupling from the past allows one to efficiently generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to nonattractive distributions by the use of summary states, as first described by Huber. Using this method, we present exact samples from a frustrated antiferromagnetic triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss the advantages and limitations of the method of summary states for practical sampling, paying particular attention to the slowing down of the algorithm at low temperature. In particular, we show that such slowing down can occur in the absence of a physical phase transition.