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

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 τint,E ≥ const × CH is almost, but not quite sharp. The ratio τint,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 τexp,E is proportional to the integrated autocorrelation time τint,E . Running title: Dynamic Critical Behavior of Cluster Algorithms