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

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

Comments: 51062 bytes uuencoded gzip'ed (expands to 111127 bytes Postscript); 4 pages including all figures; contribution to Lattice '95