{
  "id": "1807.05020",
  "version": "v1",
  "published": "2018-07-13T11:49:51.000Z",
  "updated": "2018-07-13T11:49:51.000Z",
  "title": "Critical Regime in a Curie-Weiss Model with two Groups and Heterogeneous Coupling",
  "authors": [
    "Werner Kirsch",
    "Gabor Toth"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss a Curie-Weiss model with two groups in the critical regime. This is the region where the central limit theorem does not hold any more but the mean magnetization still goes to zero as the number of spins grows. We show that the total magnetization normalized by $N^{3/4}$ converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie-Weiss model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-13T11:49:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical regime",
      "heterogeneous coupling",
      "single-group curie-weiss model",
      "central limit theorem",
      "mean magnetization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}