{
  "id": "2211.09879",
  "version": "v1",
  "published": "2022-11-17T20:34:06.000Z",
  "updated": "2022-11-17T20:34:06.000Z",
  "title": "Existence of the free energy for heavy-tailed spin glasses",
  "authors": [
    "Aukosh Jagannath",
    "Patrick Lopatto"
  ],
  "comment": "16 pages, comments welcome",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the free energy for a mean-field spin glass whose coupling distribution has power law tails. Under the assumption that the couplings have infinite variance and finite mean, we show that the limit of the quenched free energy exists, and that the free energy is self-averaging.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-17T20:34:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heavy-tailed spin glasses",
      "mean-field spin glass",
      "power law tails",
      "finite mean",
      "infinite variance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}