{
  "id": "1410.8059",
  "version": "v1",
  "published": "2014-10-29T17:08:27.000Z",
  "updated": "2014-10-29T17:08:27.000Z",
  "title": "Packing dimers on $(2p + 1) \\times (2q + 1) $ lattices",
  "authors": [
    "Yong Kong"
  ],
  "comment": "20 pages, 7 figures",
  "journal": "Physical Review E, 73, 016106 (2006)",
  "doi": "10.1103/PhysRevE.73.016106",
  "categories": [
    "cond-mat.stat-mech",
    "math.CO"
  ],
  "abstract": "We use computational method to investigate the number of ways to pack dimers on \\emph{odd-by-odd} lattices. In this case, there is always a single vacancy in the lattices. We show that the dimer configuration numbers on $(2k+1) \\times (2k+1)$ \\emph{odd} square lattices have some remarkable number-theoretical properties in parallel to those of close-packed dimers on $2k \\times 2k$ \\emph{even} square lattices, for which exact solution exists. Furthermore, we demonstrate that there is an unambiguous logarithm term in the finite size correction of free energy of odd-by-odd lattice strips with any width $n \\ge 1$. This logarithm term determines the distinct behavior of the free energy of odd square lattices. These findings reveal a deep and previously unexplored connection between statistical physics models and number theory, and indicate the possibility that the monomer-dimer problem might be solvable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-29T17:08:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.50.+q",
      "02.10.De",
      "02.70.-c"
    ],
    "keywords": [
      "packing dimers",
      "free energy",
      "dimer configuration numbers",
      "odd square lattices",
      "logarithm term determines"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2006,
      "month": "Jan",
      "volume": 73,
      "number": 1,
      "pages": "016106"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006PhRvE..73a6106K"
    }
  }
}