{
  "id": "2207.12247",
  "version": "v1",
  "published": "2022-07-25T14:56:55.000Z",
  "updated": "2022-07-25T14:56:55.000Z",
  "title": "Monotonicity of Ursell functions in the Ising model",
  "authors": [
    "Federico Camia",
    "Jianping Jiang",
    "Charles M. Newman"
  ],
  "comment": "21 pages, 10 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we consider Ising models with ferromagnetic pair interactions. We prove that the Ursell functions $u_{2k}$ satisfy: $(-1)^{k-1}u_{2k}$ is increasing in each interaction. As an application, we prove a 1983 conjecture by Nishimori and Griffiths about the partition function of the Ising model with complex external field $h$: its closest zero to the origin (in the variable $h$) moves towards the origin as an arbitrary interaction increases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-25T14:56:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ising model",
      "ursell functions",
      "monotonicity",
      "arbitrary interaction increases",
      "ferromagnetic pair interactions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}