{
  "id": "1108.3308",
  "version": "v2",
  "published": "2011-08-16T18:19:06.000Z",
  "updated": "2011-10-19T23:22:38.000Z",
  "title": "Renormalization Group Transformations Near the Critical Point: Some Rigorous Results",
  "authors": [
    "Mei Yin"
  ],
  "comment": "13 pages",
  "journal": "J. Math. Phys. 52: 113507 (2011)",
  "doi": "10.1063/1.3660381",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider renormalization group (RG) transformations for classical Ising-type lattice spin systems in the infinite volume limit. Formally, the RG maps a Hamiltonian H into a renormalized Hamiltonian H': exp(-H'(\\sigma'))=\\sum_\\sigma T(\\sigma, \\sigma')exp(-H(\\sigma)), where T(\\sigma, \\sigma') denotes a specific RG probability kernel, \\sum_\\sigma' T(\\sigma, \\sigma')=1, for every configuration \\sigma. With the help of the Dobrushin uniqueness condition and standard results on the polymer expansion, Haller and Kennedy gave a sufficient condition for the existence of the renormalized Hamiltonian in a neighborhood of the critical point. By a more complicated but reasonably straightforward application of the cluster expansion machinery, the present investigation shows that their condition would further imply a band structure on the matrix of partial derivatives of the renormalized interaction with respect to the original interaction. This in turn gives an upper bound for the RG linearization.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-19T23:22:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.50.+q",
      "05.70.Jk"
    ],
    "keywords": [
      "renormalization group transformations",
      "critical point",
      "rigorous results",
      "classical ising-type lattice spin systems",
      "specific rg probability kernel"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2011,
      "month": "Nov",
      "volume": 52,
      "number": 11,
      "pages": 3507
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 924124,
      "adsabs": "2011JMP....52k3507Y"
    }
  }
}