{
  "id": "1512.05404",
  "version": "v1",
  "published": "2015-12-16T22:52:08.000Z",
  "updated": "2015-12-16T22:52:08.000Z",
  "title": "Constraint percolation on hyperbolic lattices",
  "authors": [
    "Jorge H. Lopez",
    "J. M. Schwarz"
  ],
  "comment": "10 pages, 15 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices and are interesting in their own right with ordinary percolation exhibiting not one, but two, phase transitions. We study four constraint percolation models---$k$-core percolation (for $k=1,2,3$) and force-balance percolation---on several tessellations of the hyperbolic plane. By comparing these four different models, our numerical data suggests that all of the $k$-core models, even for $k=3$, exhibit behavior similar to ordinary percolation, while the force-balance percolation transition is discontinuous. We also provide a proof, for some hyperbolic lattices, of the existence of a critical probability that is less than unity for the force-balance model, so that we can place our interpretation of the numerical data for this model on a more rigorous footing. Finally, we discuss improved numerical methods for determining the two critical probabilities on the hyperbolic lattice for the $k$-core percolation models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-16T22:52:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "82B26",
      "51M10"
    ],
    "keywords": [
      "constraint percolation",
      "ordinary percolation",
      "critical probability",
      "core percolation models",
      "force-balance percolation transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151205404L"
    }
  }
}