{
  "id": "2206.13126",
  "version": "v1",
  "published": "2022-06-27T09:08:04.000Z",
  "updated": "2022-06-27T09:08:04.000Z",
  "title": "Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus",
  "authors": [
    "Jesús Salas",
    "Alan D. Sokal"
  ],
  "comment": "26 pages, pdflatex, and 22 pdf figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We prove the ergodicity of the Wang--Swendsen--Koteck\\'y (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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-27T09:08:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodicity",
      "state potts antiferromagnet",
      "eulerian triangulation",
      "wsk algorithm",
      "sublattice consists"
    ],
    "note": {
      "typesetting": "PDFLaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}