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

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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 int, E ≥ const × Cₕ is almost, but not quite sharp. The ratio τ int, E/Cₕ appears to tend to infinity either as a logarithm or as a small power (0.05 p 0.12). We also show that the exponential autocorrelation time τ exp, E is proportional to the integrated autocorrelation time τ int, E.