{
  "id": "2303.12453",
  "version": "v1",
  "published": "2023-03-22T10:44:09.000Z",
  "updated": "2023-03-22T10:44:09.000Z",
  "title": "Ising model with a magnetic field",
  "authors": [
    "K. A. Meissner",
    "D. Ircha",
    "W. Olszewski",
    "J Ruta",
    "A. Słapek"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The paper presents the low temperature expansion of the 2D Ising model in the presence of the magnetic field in powers of $x=\\exp(-J/(kT))$ and $z=\\exp(B/(kT))$ with full polynomials in $z$ up to $x^{88}$ and full polynomials in $x^4$ up to $z^{-60}$, in the latter case the polynomials are explicitly given. The new result presented in the paper is an expansion not in inverse powers of $z$ but in $(z^2+x^8)^{-k}$ where the subsequent coefficients (polynomials in $x^4$) turn out to be divisible by increasing powers of $(1-x^4)$. The paper describes both the analytic expansions of the partition function and the efficient combinatorial methods to get the coefficients of the expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-22T10:44:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic field",
      "full polynomials",
      "low temperature expansion",
      "efficient combinatorial methods",
      "2d ising model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}