{
  "id": "2408.14184",
  "version": "v1",
  "published": "2024-08-26T11:18:23.000Z",
  "updated": "2024-08-26T11:18:23.000Z",
  "title": "Bounds in partition functions of the continuous random field Ising model",
  "authors": [
    "G. O. Heymans",
    "N. F. Svaiter",
    "B. F. Svaiter",
    "A. M. S. Macêdo"
  ],
  "comment": "6 pages",
  "categories": [
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the critical properties of continuous random field Ising model (RFIM). Using the distributional zeta-function method, we obtain a series representation for the quenched free energy. It is possible to show that for each moment of the partition function, the multiplet of $k$-fields the Gaussian contribution has one field with the contribution of the disorder and $(k-1)$-fields with the usual propagator. Although the non-gaussian contribution is non-perturbative we are able to show that the model is confined between two $\\mathbb{Z}_2\\times\\mathcal{O}(k-1)$-symmetric models. Using arguments of lower critical dimension alongside with monotone operators, we show that the phase of the continuous RFIM can be restricted by an $\\mathbb{Z}_2 \\times \\mathcal{O}(k-1) \\to \\mathcal{O}(k-2)$ phase transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-26T11:18:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous random field ising model",
      "partition function",
      "lower critical dimension alongside",
      "distributional zeta-function method",
      "contribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}