Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus

Abstract

We prove the ergodicity of the Wang--Swendsen--Kotecký (WSK) algorithm for the zero-temperature $q$-state Potts antiferromagnet on several classes of lattices on the torus. In particular, the WSK algorithm is ergodic for $q\ge 4$ on any quadrangulation of the torus of girth $\ge 4$. It is also ergodic for $q\ge 5$ (resp. $q\ge 3$) on any Eulerian triangulation of the torus such that one sublattice consists of degree-4 vertices while the other two sublattices induce a quadrangulation of girth $\ge 4$ (resp.~a bipartite quadrangulation) of the torus. These classes include many lattices of interest in statistical mechanics.

arXiv comment27 pages, pdflatex, and 22 pdf figures. Corrected an error in Remark 4 after Theorem 4.4. Final version

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