Dynamic Critical Behavio(u)r of a Cluster 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, revealing that the Li--Sokal bound holds but is not tight, with autocorrelation times growing faster than specific heat.

Contribution

It provides the first detailed analysis of the autocorrelation times and bounds for a cluster algorithm on the Ashkin--Teller model, highlighting the non-sharpness of the Li--Sokal bound.

Findings

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

Autocorrelation time ratio diverges logarithmically or as a small power

Bound is not sharp, indicating slower decay of autocorrelations

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, but this bound is apparently not sharp. The ratio $\tau_{{\rm int},{\cal E}}/C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \ltapprox p \ltapprox 0.12$).