{
  "id": "1904.09168",
  "version": "v1",
  "published": "2019-04-19T12:36:29.000Z",
  "updated": "2019-04-19T12:36:29.000Z",
  "title": "Magnetization in the zig-zag layered Ising model and orthogonal polynomials",
  "authors": [
    "Dmitry Chelkak",
    "Clément Hongler",
    "Rémy Mahfouf"
  ],
  "comment": "34 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "math.SP"
  ],
  "abstract": "We discuss the magnetization $M_m$ in the $m$-th column of the zig-zag layered 2D Ising model on a half-plane using Kadanoff-Ceva fermions and orthogonal polynomials techniques. Our main result gives an explicit representation of $M_m$ via $m\\times m$ Hankel determinants constructed from the spectral measure of a certain Jacobi matrix which encodes the interaction parameters between the columns. We also illustrate our approach by giving short proofs of the classical Kaufman-Onsager-Yang and McCoy-Wu theorems in the homogeneous setup and expressing $M_m$ as a Toeplitz+Hankel determinant for the homogeneous sub-critical model in presence of a boundary magnetic field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-19T12:36:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "47B36",
      "33C47"
    ],
    "keywords": [
      "zig-zag layered ising model",
      "magnetization",
      "zig-zag layered 2d ising model",
      "orthogonal polynomials techniques",
      "boundary magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}