{
  "id": "cond-mat/0410045",
  "version": "v5",
  "published": "2004-10-02T06:37:15.000Z",
  "updated": "2005-01-26T02:45:30.000Z",
  "title": "Nonextensive thermodynamics of the two-site Hubbard model",
  "authors": [
    "Hideo Hasegawa"
  ],
  "comment": "22 pages, 7 figures, accepted in Physica A with minor changes",
  "journal": "Physica A 351 (2005) 273.",
  "doi": "10.1016/j.physa.2005.01.025",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mes-hall"
  ],
  "abstract": "Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature $T$ to the Lagrange multiplier $\\beta$, two methods have been adopted: $T=1/k_B \\beta$ in the method A [Tsallis {\\it et al.} Physica A {\\bf 261} (1998) 534], and $T=c_q/k_B \\beta$ in the method B [Abe {\\it et al.} Phys. Lett. A {\\bf 281} (2001) 126], where $k_B$ denotes the Boltzman constant, $c_q= \\sum_i p_i^q$, $p_i$ the probability distribution of the $i$th state, and $q$ the entropic index. Temperature dependences of specific heat and magnetic susceptibility have been calculated for $1 \\lleq q \\lleq 2$, the conventional Boltzman-Gibbs statistics being recovered in the limit of $q = 1$. The Curie constant $\\Gamma_q$ of the susceptibility in the atomic and low-temperature limits ($t/U \\to 0, T/U \\to 0$) is shown to be given by $\\Gamma_q=2 q 2^{2(q-1)}$ in the method A, and $\\Gamma_q=2 q$ in the method B, where $t$ stands for electron hoppings and $U$ intra-atomic interaction in the Hubbard model. These expressions for $\\Gamma_q$ are shown to agree with the results of a free spin model which has been studied also by the NES with the methods A and B. A comparison has been made between the results for canonical and grand-canonical ensembles of the model.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2005-01-26T02:45:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonextensive thermodynamics",
      "free spin model",
      "grand-canonical ensembles",
      "half-filled two-site hubbard model",
      "conventional boltzman-gibbs statistics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}