{
  "id": "1311.1502",
  "version": "v2",
  "published": "2013-11-06T09:59:19.000Z",
  "updated": "2015-12-18T14:35:52.000Z",
  "title": "Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket",
  "authors": [
    "Meng Wang",
    "Shi-Ju Ran",
    "Tao Liu",
    "Yang Zhao",
    "Qing-Rong Zheng",
    "Gang Su"
  ],
  "comment": "9 pages, 12 figures",
  "doi": "10.1140/epjb/e2015-60745-5",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "The anisotropic antiferromagnetic Ising model on the fractal Sierpi\\'{n}ski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \\leq$J$_b/$J$_a<1$, and an interesting crossover behavior between different phases at J$_b/$J$_a=1$ is unveiled, whose dynamics can be described by the J$_b/$J$_a$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi\\'{n}ski gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpi\\'{n}ski gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-06T09:59:19.000Z",
      "title": "Phase diagram and exotic spin-spin correlations of J$_1$-J$_2$ Ising model on the Sierpiński gasket",
      "abstract": "The J$_1$-J$_2$ antiferromagnetic Ising model on the fractal Sierpi\\'nski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained, where three nontrivial phases including the $1/3$ magnetization plateau ordered and disordered phases, and the $5/9$ plateau partially ordered phase, as well as five boundaries and two intersection points are accurately identified in terms of the uniform and subset magnetization and the residual entropy as well. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations, where some interesting features due to the special geometry of the Sierpi\\'nski gasket are discovered. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \\leq$J$_2/$J$_1<1$, and an interesting crossover behavior between different phases at J$_2/$J$_1=1$ is unveiled, whose dynamics can be described by the J$_2/$J$_1$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi\\'nski gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered phase.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Shi-Ju Ran",
        "Tao Liu",
        "Yang Zhao",
        "Gang Su"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-12-18T14:35:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ising model",
      "sierpiński gasket",
      "plateau partially ordered phase",
      "sierpinski gasket",
      "ground state phase diagram"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1263829,
      "adsabs": "2013arXiv1311.1502W"
    }
  }
}