{
  "id": "1305.5323",
  "version": "v1",
  "published": "2013-05-23T06:25:44.000Z",
  "updated": "2013-05-23T06:25:44.000Z",
  "title": "Realization of stripes and slabs in two and three dimensions",
  "authors": [
    "Alessandro Giuliani",
    "Elliott H. Lieb",
    "Robert Seiringer"
  ],
  "comment": "4 pages, 1 figure",
  "journal": "Phys. Rev. B 88, 064401 (2013)",
  "doi": "10.1103/PhysRevB.88.064401",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long range, power law decaying, antiferromagnetic interactions. If the strength of the ferromagnetic coupling J is larger than a critical value J_c, then the ground state is homogeneous and ferromagnetic. As the critical value is approached from smaller values of J, it is believed that the ground state consists of a periodic array of stripes (d=2) or slabs (d=3), all of the same size and alternating magnetization. Here we prove rigorously that the ground state energy per site converges to that of the optimal periodic striped/slabbed state, in the limit that J tends to the ferromagnetic transition point. While this theorem does not prove rigorously that the ground state is precisely striped/slabbed, it does prove that in any suitably large box the ground state is striped/slabbed with high probability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-23T06:25:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "75.10.Hk",
      "05.50.+q",
      "75.70.Kw",
      "89.75.Kd"
    ],
    "keywords": [
      "dimensions",
      "nearest neighbor ferromagnetic interactions",
      "realization",
      "ground state energy",
      "critical value"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2013,
      "month": "Aug",
      "volume": 88,
      "number": 6,
      "pages": "064401"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvB..88f4401G"
    }
  }
}