{
  "id": "2305.13561",
  "version": "v1",
  "published": "2023-05-23T00:21:35.000Z",
  "updated": "2023-05-23T00:21:35.000Z",
  "title": "Binary fluid in a random medium and dimensional transmutation",
  "authors": [
    "John Cardy"
  ],
  "comment": "4 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We propose a solution to the puzzle of dimensional reduction in the random field Ising model by studying the equivalent binary fluid in a random medium, and inverting the question by asking: to what random problem in $D\\!=\\!d+2$ dimensions does a pure system in $d$ dimensions correspond? For a model with purely repulsive interactions of finite range, we show that the mean density and other observables are equal to those of a similar model in $D$ dimensions, but with interactions and correlated disorder in the extra two dimensions of range $\\propto\\lambda$, in the limit as $\\lambda\\to\\infty$. There is no conflict with rigorous results that the finite range model with locally correlated disorder orders in $D=3$. Our argument avoids the use of replicas and perturbative field theory, instead being based on convergent cluster expansions. Although the result may be seen as a consequence of Parisi-Sourlas supersymmetry, it follows more directly from Kirchhoff's matrix-tree theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-23T00:21:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random medium",
      "dimensional transmutation",
      "dimensions",
      "equivalent binary fluid",
      "random field ising model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}