{
  "id": "2412.17662",
  "version": "v1",
  "published": "2024-12-23T15:39:59.000Z",
  "updated": "2024-12-23T15:39:59.000Z",
  "title": "Ising model in the Rényi statistics: the finite size effects",
  "authors": [
    "V. V. Ignatyuk",
    "A. P. Moina"
  ],
  "comment": "20 pages, 9 figures (Accepted version)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The R\\'{e}nyi statistics is applied for a description of finite size effects in the 1D Ising model. We calculate the internal energy of the spin chain and the system temperature using the R\\'{e}nyi distribution and postulate them to be equal to their counterparts, obtained in the microcanonical ensemble. It allows us to self-consistently derive the R\\'{e}nyi $q$-index and the Lagrange parameter $T$ to relate them to the physically observed system temperature $T_{\\rm ph}$, and to show that the entropic phase transitions are possible in a broad temperature domain. We have also studied the temperature dependence of the internal energy $U(T_{\\rm ph})$ at constant $q$ and an influence of the size related effects on the system thermodynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-23T15:39:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite size effects",
      "rényi statistics",
      "internal energy",
      "system temperature",
      "entropic phase transitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}