{
  "id": "cond-mat/0007254",
  "version": "v2",
  "published": "2000-07-14T20:54:38.000Z",
  "updated": "2000-12-18T21:32:12.000Z",
  "title": "Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry",
  "authors": [
    "Ilya A. Gruzberg",
    "N. Read",
    "Andreas W. W. Ludwig"
  ],
  "comment": "28 pages; largely independent of cond-mat/0007255. V. 2: small additions, references updated; as published",
  "journal": "Phys. Rev. B 63, 104422 (2001).",
  "doi": "10.1103/PhysRevB.63.104422",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mes-hall"
  ],
  "abstract": "We consider a classical random-bond Ising model (RBIM) with binary distribution of $\\pm K$ bonds on the square lattice at finite temperature. In the phase diagram of this model there is the so-called Nishimori line which intersects the phase boundary at a multicritical point. It is known that the correlation functions obey many exact identities on this line. We use a supersymmetry method to treat the disorder. In this approach the transfer matrices of the model on the Nishimori line have an enhanced supersymmetry osp($2n+1|2n$), in contrast to the rest of the phase diagram, where the symmetry is osp($2n|2n$) (where $n$ is an arbitrary positive integer). An anisotropic limit of the model leads to a one-dimensional quantum Hamiltonian describing a chain of interacting superspins, which are irreducible representations of the osp($2n+1|2n$) superalgebra. By generalizing this superspin chain, we embed it into a wider class of models. These include other models that have been studied previously in one and two dimensions. We suggest that the multicritical behavior in two dimensions of a class of these generalized models (possibly not including the multicritical point in the RBIM itself) may be governed by a single fixed point, at which the supersymmetry is enhanced still further to osp($2n+2|2n$). This suggestion is supported by a calculation of the renormalization-group flows for the corresponding nonlinear sigma models at weak coupling.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-12-18T21:32:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nishimori line",
      "supersymmetry",
      "dimensions",
      "phase diagram",
      "corresponding nonlinear sigma models"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}