{
  "id": "2303.09654",
  "version": "v1",
  "published": "2023-03-16T21:21:36.000Z",
  "updated": "2023-03-16T21:21:36.000Z",
  "title": "Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction",
  "authors": [
    "Slava Rychkov"
  ],
  "comment": "55 pages, 11 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any $d$. These notes give a leisurely introduction to a recent theory, developed jointly with A. Kaviraj and E. Trevisani, which aims to explain these facts. Based on the lectures given in Cortona and at the IHES in 2022.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T21:21:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random field ising model",
      "dimensional reduction",
      "model loses parisi-sourlas susy",
      "parisi-sourlas supersymmetry",
      "field ising model loses parisi-sourlas"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}