Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model

Abstract

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time (${\tau }_{\mathrm{int},\mathcal{E}}\ge \mathrm{const}\times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio ${\tau }_{\mathrm{int},\mathcal{E}}/C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05\le p\le 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.

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