{
  "id": "0707.0688",
  "version": "v1",
  "published": "2007-07-04T20:54:47.000Z",
  "updated": "2007-07-04T20:54:47.000Z",
  "title": "Dependence of ground state energy of classical n-vector spins on n",
  "authors": [
    "Samarth Chandra"
  ],
  "comment": "6 pages, 2 figures, submitted to Physical Review E",
  "doi": "10.1103/PhysRevE.77.021125",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the ground state energy E_G(n) of N classical n-vector spins with the hamiltonian H = - \\sum_{i>j} J_ij S_i.S_j where S_i and S_j are n-vectors and the coupling constants J_ij are arbitrary. We prove that E_G(n) is independent of n for all n > n_{max}(N) = floor((sqrt(8N+1)-1) / 2) . We show that this bound is the best possible. We also derive an upper bound for E_G(m) in terms of E_G(n), for m<n. We obtain an upper bound on the frustration in the system, as measured by F(n), which is defined to be (\\sum_{i>j} |J_ij| + E_G(n)) / (\\sum_{i>j} |J_ij|). We describe a procedure for constructing a set of J_ij's such that an arbitrary given state, {S_i}, is the ground state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-04T20:54:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.20.-y",
      "75.10.Hk"
    ],
    "keywords": [
      "ground state energy",
      "classical n-vector spins",
      "dependence",
      "upper bound",
      "independent"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2008,
      "month": "Feb",
      "volume": 77,
      "number": 2,
      "pages": "021125"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvE..77b1125C"
    }
  }
}