{
  "id": "2006.06654",
  "version": "v1",
  "published": "2020-06-11T17:48:32.000Z",
  "updated": "2020-06-11T17:48:32.000Z",
  "title": "Exponential decay of transverse correlations for spin systems with continuous symmetry and non-zero external field",
  "authors": [
    "Benjamin Lees",
    "Lorenzo Taggi"
  ],
  "comment": "26 pages, 2 Figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N > 1. Our result is new when N > 3, in which case no Lee-Yang theorem is available, it is an alternative to Lee-Yang when N = 2, 3, and also holds for a wide class of multi-component spin systems with continuous symmetry. The key ingredients are a representation of the model as a system of coloured random paths, a `colour-switch' lemma, and a sampling procedure which allows us to bound from above the `typical' length of the open paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-11T17:48:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "60K35",
      "82B26"
    ],
    "keywords": [
      "non-zero external field",
      "exponential decay",
      "transverse correlations",
      "continuous symmetry",
      "arbitrary spin dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}