{
  "id": "2406.12728",
  "version": "v1",
  "published": "2024-06-18T15:49:21.000Z",
  "updated": "2024-06-18T15:49:21.000Z",
  "title": "Towrad mean-field bound for critical temperature on Nishimori line",
  "authors": [
    "Manaka Okuyama",
    "Masayuki Ohzeki"
  ],
  "comment": "9pages, 0 figure",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "The critical inverse temperature of the mean-field approximation gives a lower bound of the true critical inverse temperature in a broad class of ferromagnetic spin models, which is called the mean-field bound for the critical temperature. In this study, we explore the possibility of a corresponding mean-field bound for the critical temperature in Ising spin-glass models with Gaussian randomness on the Nishimori line. On the Nishimori line, the critical inverse temperature of the mean-field approximation is given by $\\beta_{MF}^{NL}=\\sqrt{1/z}$, where $z$ denotes the coordination number. Using the Griffiths inequalities on the Nishimori line, we prove that there is zero spontaneous magnetization in the high-temperature region $\\beta < \\beta_{MF}^{NL}/2$. In other words, the true critical inverse temperature $\\beta_c^{NL}$ of the Nishimori line is always bounded by $\\beta_c^{NL} \\ge \\beta_{MF}^{NL}/2$. Unfortunately, we did not succeed in obtaining the corresponding mean-field bound $\\beta_c^{NL} \\ge \\beta_{MF}^{NL}$ on the Nishimori line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-18T15:49:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nishimori line",
      "towrad mean-field bound",
      "critical temperature",
      "true critical inverse temperature",
      "corresponding mean-field bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}