{
  "id": "cond-mat/0305131",
  "version": "v1",
  "published": "2003-05-07T12:05:10.000Z",
  "updated": "2003-05-07T12:05:10.000Z",
  "title": "Comment on ``Renormalization-group picture of the Lifshitz critical behavior''",
  "authors": [
    "H. W. Diehl",
    "M. Shpot"
  ],
  "comment": "A comment on M. Leite, Phys Rev B 67, 104415 (2003) revtex4, 2 pages",
  "journal": "Phys.Rev. BD68 (2003) 066401; Phys.Rev. B67 (2003) 104415",
  "doi": "10.1103/PhysRevB.68.066401",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "hep-th"
  ],
  "abstract": "We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B {\\bf 67}, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not give an ultraviolet finite renormalized theory, is plagued by inconsistencies, misses the existence of a nontrivial anisotropy exponent $\\theta\\ne 1/2$, and therefore yields incorrect hyperscaling relations. His $\\epsilon$-expansion results to order $\\epsilon^2$ for the critical exponents of $m$-axial Lifshitz points are incorrect both in the anisotropic ($0<m<d$) and the isotropic cases ($m=d$). The inherent inconsistencies and the lack of a sound basis of the approach makes its results unacceptable even if they are interpreted in the sense of approximations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-07T12:05:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lifshitz critical behavior",
      "renormalization-group picture",
      "axial lifshitz points",
      "yields incorrect hyperscaling relations",
      "nontrivial anisotropy exponent"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. B"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 623736
    }
  }
}