{
  "id": "cond-mat/0406216",
  "version": "v2",
  "published": "2004-06-09T10:05:08.000Z",
  "updated": "2004-09-02T20:10:03.000Z",
  "title": "Boundary critical behaviour at $m$-axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes",
  "authors": [
    "H. W. Diehl",
    "S. Rutkevich"
  ],
  "comment": "21 pages, one figure included as eps file, uses IOP style files",
  "journal": "J.Phys. A37 (2004) 8575-8594",
  "doi": "10.1088/0305-4470/37/36/001",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft",
    "hep-th"
  ],
  "abstract": "The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\\bm{\\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\\mathbb{R}^d$. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the $m$ potential modulation axes, with $0\\leq m\\leq d-1$, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent $\\eta_\\|^{\\rm sp}$, the surface crossover exponent $\\Phi$ and related ones are determined to first order in $\\epsilon=4+\\case{m}{2}-d$. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, $\\Phi$ is $m$-dependent already at first order in $\\epsilon$. The $\\Or(\\epsilon)$ term of $\\eta_\\|^{\\rm sp}$ is found to vanish, which implies that the difference of $\\beta_1^{\\rm sp}$ and the bulk exponent $\\beta$ is of order $\\epsilon^2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-09-02T20:10:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ud",
      "42.50.Ct"
    ],
    "keywords": [
      "axial lifshitz points",
      "surface plane parallel",
      "boundary critical behaviour",
      "modulation axes",
      "special transition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2004,
      "month": "Sep",
      "volume": 37,
      "number": 36,
      "pages": 8575
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 652304,
      "adsabs": "2004JPhA...37.8575D"
    }
  }
}