{
  "id": "cond-mat/0605568",
  "version": "v1",
  "published": "2006-05-23T12:06:36.000Z",
  "updated": "2006-05-23T12:06:36.000Z",
  "title": "Recursion relations for the partition function of the two-dimensional Ising model",
  "authors": [
    "Michael Kastner"
  ],
  "comment": "7 pages, no figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function consisting of four summands. The summands are rewritten as functions of a low-temperature expansion variable, resulting in polynomials with integer coefficients. Considering these polynomials for system sizes $2^m\\times 2^n$ ($m,n\\in\\N$), a variety of recursion relations in $m,n$ are found. The recursions reveal a rich structure of the partition function and can be employed to render the computer algebra calculation of the microcanonical partition function more efficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-23T12:06:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional ising model",
      "recursion relations",
      "computer algebra calculation",
      "periodic boundary conditions",
      "nearest-neighbour interactions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006cond.mat..5568K"
    }
  }
}