{
  "id": "1602.08681",
  "version": "v1",
  "published": "2016-02-28T08:12:22.000Z",
  "updated": "2016-02-28T08:12:22.000Z",
  "title": "Critical exponents and the pseudo-$ε$ expansion",
  "authors": [
    "M. A. Nikitina",
    "A. I. Sokolov"
  ],
  "comment": "18 pages, 10 tables",
  "journal": "Teor. Mat. Fiz. 186, 230 (2016) [Theor. Math. Phys. 186, 192 (2016)]",
  "doi": "10.1134/S0040577916020057 10.4213/tmf8966",
  "categories": [
    "cond-mat.stat-mech",
    "hep-lat",
    "hep-th"
  ],
  "abstract": "We present the pseudo-$\\epsilon$ expansions ($\\tau$-series) for the critical exponents of a $\\lambda\\phi^4$ three-dimensional $O(n)$-symmetric model obtained on the basis of six-loop renormalization-group expansions. Concrete numerical results are presented for physically interesting cases $n = 1$, $n = 2$, $n = 3$ and $n = 0$, as well as for $4 \\le n \\le 32$ in order to clarify the general properties of the obtained series. The pseudo-$\\epsilon$-expansions for the exponents $\\gamma$ and $\\alpha$ have small and rapidly decreasing coefficients. So, even the direct summation of the $\\tau$-series leads to fair estimates for critical exponents, while addressing Pade approximants enables one to get high-precision numerical results. In contrast, the coefficients of the pseudo-$\\epsilon$ expansion of the scaling correction exponent $\\omega$ do not exhibit any tendency to decrease at physical values of $n$. But the corresponding series are sign-alternating, and to obtain reliable numerical estimates, it also suffices to use simple Pad\\'e approximants in this case. The pseudo-$\\epsilon$ expansion technique can therefore be regarded as a specific resummation method converting divergent renormalization-group series into expansions that are computationally convenient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-28T08:12:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponents",
      "resummation method converting divergent renormalization-group",
      "method converting divergent renormalization-group series",
      "specific resummation method converting divergent",
      "addressing pade approximants enables"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Theoretical and Mathematical Physics",
      "year": 2016,
      "month": "Feb",
      "volume": 186,
      "number": 2,
      "pages": 192
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016TMP...186..192N",
      "inspire": 1424847
    }
  }
}