Ergodicity of the Wang-Swendsen-Kotecký algorithm on several classes of lattices on the torus Articles
- October 2022
Digital Object Identifier (DOI)
- 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.
- eulerian triangulations; quadrangulations; torus; kempe chains; antiferromagnetic potts model; wang-swendsen-kotecký algorithm; ergodicity