{
  "id": "cond-mat/0309576",
  "version": "v1",
  "published": "2003-09-25T07:45:17.000Z",
  "updated": "2003-09-25T07:45:17.000Z",
  "title": "Parisi States in a Heisenberg Spin-Glass Model in Three Dimensions",
  "authors": [
    "F. Matsubara",
    "T. Shirakura",
    "Y. Baba"
  ],
  "comment": "4 pages, 6 figures",
  "doi": "10.1088/0305-4470/37/9/L01",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "We have studied low-lying metastable states of the $\\pm J$ Heisenberg model in two ($d=2$) and three ($d=3$) dimensions having developed a hybrid genetic algorithm. We have found a strong evidence of the occurrence of the Parisi states in $d=3$ but not in $d=2$. That is, in $L^d$ lattices, there exist metastable states with a finite excitation energy of $\\Delta E \\sim O(J)$ for $L \\to \\infty$, and energy barriers $\\Delta W$ between the ground state and those metastable states are $\\Delta W \\sim O(JL^{\\theta})$ with $\\theta > 0$ in $d=3$ but with $\\theta < 0$ in $d=2$. We have also found droplet-like excitations, suggesting a mixed scenario of the replica-symmetry-breaking picture and the droplet picture recently speculated in the Ising SG model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-25T07:45:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg spin-glass model",
      "parisi states",
      "dimensions",
      "metastable states",
      "hybrid genetic algorithm"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}