{
  "id": "2012.08204",
  "version": "v2",
  "published": "2020-12-15T10:51:18.000Z",
  "updated": "2021-01-05T11:29:46.000Z",
  "title": "Fluctuations of the Magnetization for Ising models on Erdős-Rényi Random Graphs -- the Regimes of Low Temperature and External Magnetic Field",
  "authors": [
    "Zakhar Kabluchko",
    "Matthias Löwe",
    "Kristina Schubert"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We continue our analysis of Ising models on the (directed) Erd\\H{o}s-R\\'enyi random graph $G(N,p)$. We prove a quenched Central Limit Theorem for the magnetization and describe the fluctuations of the log-partition function. In the current note we consider the low temperature regime $\\beta>1$ and the case when an external magnetic field is present. In both cases, we assume that $p=p(N)$ satisfies $p^3N \\to \\infty$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-01-05T11:29:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82B20"
    ],
    "keywords": [
      "external magnetic field",
      "erdős-rényi random graphs",
      "ising models",
      "magnetization",
      "fluctuations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}