{
  "id": "1803.10155",
  "version": "v2",
  "published": "2018-03-27T16:00:26.000Z",
  "updated": "2019-06-24T13:50:52.000Z",
  "title": "Anisotropic scaling of the two-dimensional Ising model I: the torus",
  "authors": [
    "Hendrik Hobrecht",
    "Alfred Hucht"
  ],
  "comment": "34 pages, 10 figures, submitted to SciPost.org, revised version, text and references added, several errors fixed",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and - if present - the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-06-24T13:50:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional ising model",
      "square lattice ising model",
      "two-dimensional square lattice ising",
      "anisotropic scaling",
      "energy finite-size scaling functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}