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

TL;DR

This paper investigates the dynamic critical behavior of a Swendsen-Wang-type algorithm applied to the Ashkin-Teller model, confirming the Li--Sokal bound and analyzing autocorrelation times near criticality.

Contribution

It provides the first detailed analysis of autocorrelation times for this algorithm on the Ashkin-Teller model, including the near-sharpness of the Li--Sokal bound.

Findings

Li--Sokal bound holds along the self-dual curve

Autocorrelation time ratio tends to infinity logarithmically or as a small power

The bound is almost but not quite sharp

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 ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \leq p \leq 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.