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

publication date

  • October 2022

start page

  • 1

end page

  • 22


  • 55


  • 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.


  • Physics


  • eulerian triangulations; quadrangulations; torus; kempe chains; antiferromagnetic potts model; wang-swendsen-kotecký algorithm; ergodicity