Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models

Details Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models Dynamic critical behavior of cluster algorithms for 2D Ashkin-Teller and Potts models

2000-04-19

arxiv.org/abs/cond-mat/0004329v1

Markov Process. Related Fields 7 (2001) 55-74

Physics

Condensed Matter

Statistical Mechanics

19 pages, LaTeX2e. Self-unpacking file containing the tex file, three macros and four ps files. Talk presented at the conferen

Scientific paper

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 \tau_{{\rm int},{\cal E}} \geq const \times C_H is almost, but not quite sharp. The ratio \tau_{{\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 \tau_{{\rm exp},{\cal E}} is proportional to the integrated autocorrelation time \tau_{{\rm int},{\cal E}}.

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