{
  "id": "1402.3894",
  "version": "v2",
  "published": "2014-02-17T05:36:29.000Z",
  "updated": "2014-03-31T05:45:08.000Z",
  "title": "Fisher Exponent from Pseudo-$ε$ Expansion",
  "authors": [
    "A. I. Sokolov",
    "M. A. Nikitina"
  ],
  "comment": "14 pages, 4 tables, 1 figure; figure added, one number in Table IV corrected",
  "journal": "Phys. Rev. E 90, 012102 (2014)",
  "categories": [
    "cond-mat.stat-mech",
    "hep-lat",
    "hep-ph",
    "hep-th"
  ],
  "abstract": "Critical exponent $\\eta$ for three-dimensional systems with $n$-vector order parameter is evaluated in the frame of pseudo-$\\epsilon$ expansion approach. Pseudo-$\\epsilon$ expansion ($\\tau$-series) for $\\eta$ found up to $\\tau^7$ term for $n$ = 0, 1, 2, 3 and within $\\tau^6$ order for general $n$ is shown to have a structure rather favorable for getting numerical estimates. Use of Pad\\'e approximants and direct summation of $\\tau$-series result in iteration procedures rapidly converging to the asymptotic values that are very close to most reliable numerical estimates of $\\eta$ known today. The origin of this fortune is discussed and shown to lie in general properties of the pseudo-$\\epsilon$ expansion machinery interfering with some peculiarities of the renormalization group expansion of $\\eta$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-31T05:45:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Jk",
      "05.10.Cc",
      "64.60.ae"
    ],
    "keywords": [
      "fisher exponent",
      "renormalization group expansion",
      "vector order parameter",
      "expansion machinery",
      "general properties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "doi": "10.1103/PhysRevE.90.012102",
      "year": 2014,
      "month": "Jul",
      "volume": 90,
      "number": 1,
      "pages": "012102"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1281687,
      "adsabs": "2014PhRvE..90a2102S"
    }
  }
}