{
  "id": "cond-mat/0004161",
  "version": "v2",
  "published": "2000-04-11T22:12:44.000Z",
  "updated": "2000-04-14T21:30:04.000Z",
  "title": "Ground State Entropy of the Potts Antiferromagnet on Strips of the Square Lattice",
  "authors": [
    "Shu-Chiuan Chang",
    "Robert Shrock"
  ],
  "comment": "37 pages, latex, 4 encapsulated postscript figures",
  "journal": "Physica A290 (2001) 402-430",
  "doi": "10.1016/S0378-4371(00)00457-X",
  "categories": [
    "cond-mat.stat-mech",
    "hep-lat",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present exact solutions for the zero-temperature partition function (chromatic polynomial $P$) and the ground state degeneracy per site $W$ (= exponent of the ground-state entropy) for the $q$-state Potts antiferromagnet on strips of the square lattice of width $L_y$ vertices and arbitrarily great length $L_x$ vertices. The specific solutions are for (a) $L_y=4$, $(FBC_y,PBC_x)$ (cyclic); (b) $L_y=4$, $(FBC_y,TPBC_x)$ (M\\\"obius); (c) $L_y=5,6$, $(PBC_y,FBC_x)$ (cylindrical); and (d) $L_y=5$, $(FBC_y,FBC_x)$ (open), where $FBC$, $PBC$, and $TPBC$ denote free, periodic, and twisted periodic boundary conditions, respectively. In the $L_x \\to \\infty$ limit of each strip we discuss the analytic structure of $W$ in the complex $q$ plane. The respective $W$ functions are evaluated numerically for various values of $q$. Several inferences are presented for the chromatic polynomials and analytic structure of $W$ for lattice strips with arbitrarily great $L_y$. The absence of a nonpathological $L_x \\to \\infty$ limit for real nonintegral $q$ in the interval $0 < q < 3$ ($0 < q < 4$) for strips of the square (triangular) lattice is discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-04-14T21:30:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state entropy",
      "square lattice",
      "analytic structure",
      "chromatic polynomial",
      "ground state degeneracy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 526347
    }
  }
}