{
  "id": "cond-mat/0506780",
  "version": "v3",
  "published": "2005-06-29T20:58:26.000Z",
  "updated": "2005-08-21T18:15:08.000Z",
  "title": "Exact Enumeration of Ground States in the Sherrington-Kirkpatrick Spin Glass",
  "authors": [
    "Stefan Boettcher",
    "Tomasz M. Kott"
  ],
  "comment": "4 pages, RevTex, 1 eps-figure included, added derivation of Gumbel distribution in SK (for related articles see http://www.physics.emory.edu/faculty/boettcher/publications.html)",
  "journal": "Phys. Rev. B 72, 212408 (2005)",
  "doi": "10.1103/PhysRevB.72.212408",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech"
  ],
  "abstract": "Using the discrete $\\pm J$ bond distribution for the Sherrington-Kirkpatrick spin glass, all ground states for the entire ensemble of the bond disorder are enumerated. Although the combinatorial complexity of the enumeration severely restricts attainable system sizes, here $N\\leq9$, some remarkably intricate patterns found in previous studies already emerge. The analysis of the exact ground state frequencies suggests a direct construction of their probability density function. Against expectations, the result suggests that its highly skewed appearance for finite $N$ evolves logarithmically slow towards a Gaussian distribution.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-08-21T18:15:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sherrington-kirkpatrick spin glass",
      "exact enumeration",
      "exact ground state frequencies",
      "severely restricts attainable system sizes",
      "probability density function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}