Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models
Abstract
Description
We study the dynamic critical behavior of two algorithms: the Swendsen-Wang algorithm for the two-dimensional Potts model with q=2,3,4 and a Swendsen-Wang-type algorithm for the two-dimensional symmetric Ashkin-Teller model on the self-dual curve. We find that the Li--Sokal bound on the autocorrelation time τ_{{\rm int},{\cal E}} \geq const \times C_H is almost, but not quite sharp. The ratio τ_{{\rm int},{\cal E}}/C_H appears to tend to infinity either as a logarithm or as a small power (0.05 \ltapprox p \ltapprox 0.12). We also show that the exponential autocorrelation time τ_{{\rm exp},{\cal E}} is proportional to the integrated autocorrelation time τ_{{\rm int},{\cal E}}.
19 pages, LaTeX2e. Self-unpacking file containing the tex file, three macros and four ps files. Talk presented at the conference on Inhomogeneous Random Systems, Université de Cergy-Pontoise, 25 January 2000. To appear in Markov Processes and Related Fields
19 pages, LaTeX2e. Self-unpacking file containing the tex file, three macros and four ps files. Talk presented at the conference on Inhomogeneous Random Systems, Université de Cergy-Pontoise, 25 January 2000. To appear in Markov Processes and Related Fields