Dynamic Critical Behavior of Cluster Algorithms for 2D Ashkin-Teller and Potts Models

#### J. Salas

2001, v.7, Issue 1, 55-74

ABSTRACT

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 $\tau_{{int},{\cal E}} \geq \hbox{const} \times C_H$ 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 < p < 0.12). We also show that the exponential autocorrelation time $\tau_{{\rm exp},{\cal E}}$ is proportional to the integrated autocorrelation time $\tau_{{\rm int},{\cal E}}$.

Keywords: Ising model,Ashkin - Teller model,Monte Carlo,Swendsen - Wangalgorithm,cluster algorithm,dynamic critical exponent,Li - Sokal bound