{
  "id": "cond-mat/0501126",
  "version": "v4",
  "published": "2005-01-07T01:47:45.000Z",
  "updated": "2005-10-31T04:11:40.000Z",
  "title": "Nonextensive thermodynamics of a cluster consisting of $M$ Hubbard dimers ($M=1,2,3$ and $\\infty$)",
  "authors": [
    "Hideo Hasegawa"
  ],
  "comment": "8 pages, 4 figures, Proceedings of International Workshop of CN-Kyoto",
  "journal": "Prog. Theor. Phys. Suppl. 162 (2006) 70",
  "doi": "10.1143/PTPS.162.70",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mes-hall"
  ],
  "abstract": "The thermodynamical property of a small cluster including $M$ Hubbard dimers, each of which is described by the two-site Hubbard model, has been discussed within the nonextensive statistics (NES). We have calculated the temperature dependence of the energy, entropy, specific heat and susceptibility for $M = 1, 2, 3$ and $\\infty$, assuming the relation between the entropic index $q$ and the cluster size $N$ given by $q=1+2/N$ ($N = 2 M$ for $M$ dimers), which was previously derived by several methods. 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, $c_q= \\sum_i p_i^q$, and $p_i$ the probability distribution of the $i$th state. The susceptibility and specific heat of spin dimers described by the Heisenberg model have been discussed also by using the NES with the methods A and B. A comparison between results calculated by the two methods suggests that the method B may be better than the method A for small-scale systems.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2005-10-31T04:11:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hubbard dimers",
      "nonextensive thermodynamics",
      "cluster consisting",
      "specific heat",
      "two-site hubbard model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}