{
  "id": "1402.4318",
  "version": "v3",
  "published": "2014-02-18T12:58:37.000Z",
  "updated": "2014-03-31T06:06:26.000Z",
  "title": "Critical Exponents of Superfluid Helium and Pseudo-$ε$ Expansion",
  "authors": [
    "A. I. Sokolov",
    "M. A. Nikitina"
  ],
  "comment": "11 pages, 4 tables; numerical estimates revised, text rewritten",
  "categories": [
    "cond-mat.stat-mech",
    "hep-lat",
    "hep-ph",
    "hep-th"
  ],
  "abstract": "Pseudo-$\\epsilon$ expansions ($\\tau$-series) for critical exponents of 3D XY model describing $\\lambda$-transition in liquid helium are derived up to $\\tau^6$ terms. Numerical estimates extracted from the $\\tau$-series obtained using Pad\\'e-Borel resummation technique, scaling relations and seven-loop ($\\tau^7$) estimate for the Fisher exponent $\\eta$ are presented including those for exponents $\\alpha$ and $\\nu$ measured in experiments with record accuracy. For the exponent $\\alpha$ the procedure argued to be most reliable gives $\\alpha= -0.0117$. This number is very close to the most accurate experimental values differing appreciably from the results of numerous lattice and field-theoretical calculations. It signals that the pseudo-$\\epsilon$ expansion is a powerful tool robust enough to evaluate critical exponents with very small absolute error. The arguments in favour of such a robustness are presented.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-31T06:06:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponents",
      "superfluid helium",
      "pade-borel resummation technique",
      "small absolute error",
      "record accuracy"
    ],
    "publication": {
      "doi": "10.1016/j.physa.2015.10.036",
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2016,
      "month": "Feb",
      "volume": 444,
      "pages": 177
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1281838,
      "adsabs": "2016PhyA..444..177S"
    }
  }
}