{
  "id": "1602.03257",
  "version": "v1",
  "published": "2016-02-10T03:55:03.000Z",
  "updated": "2016-02-10T03:55:03.000Z",
  "title": "Asymptotics of mean-field $O(N)$ models",
  "authors": [
    "Kay Kirkpatrick",
    "Tayyab Nawaz"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study mean-field classical $N$-vector models, for even integers $N\\ge 2$. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining a non-normal limit theorem at the critical temperature and central limit theorems away from the critical temperatures. Important special cases of these models are the XY ($N=2$) model of superconductors and Toy ($N=4$) model of the Higgs sector in particle physics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-10T03:55:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotics",
      "central limit theorems away",
      "important special cases",
      "critical temperature",
      "non-normal limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203257K"
    }
  }
}