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

Abstract

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 ⩾ 4 on any quadrangulation of the torus of girth ⩾ 4 . It is also ergodic for q ⩾ 5 (resp. q ⩾ 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 ⩾ 4 (resp. a bipartite quadrangulation) of the torus. These classes include many lattices of interest in statistical mechanics.