Dynamic Critical Behavio(u)r of a Cluster Algorithm for the Ashkin--Teller Model

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 (${\tau }_{\mathrm{i}\mathrm{n}\mathrm{t},\mathcal{E}}\ge \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\times C_H$) holds along the self-dual curve of the symmetric Ashkin–Teller model, but this bound is apparently not sharp. The ratio ${\tau }_{\mathrm{i}\mathrm{n}\mathrm{t},\mathcal{E}}\mathrm{/}{C}_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \ltapprox p \ltapprox 0.12$).