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.

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

References in corpus (5)

• Classifying Potts critical lines
• Phase transition in the 3-state Potts antiferromagnet on the diced lattice
• On the non-ergodicity of the Swendsen-Wang-Kotecky algorithm on the kagome lattice
• Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet