{
  "id": "1602.02324",
  "version": "v1",
  "published": "2016-02-07T00:55:06.000Z",
  "updated": "2016-02-07T00:55:06.000Z",
  "title": "Critical exponent $η$ in 2D $O(N)$-symmetric $\\varphi^4$-model up to 6~loops",
  "authors": [
    "L. Ts. Adzhemyan",
    "Yu. V. Kirienko",
    "M. V. Kompaniets"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Critical exponent $\\eta$ (Fisher exponent) in $O(N)$-symmetric $\\varphi^4$-model was calculated using renormalization group approach in the space of fixed dimension $D=2$ up to 6~loops. The calculation of the renormalization constants was performed with the use of $R'$-operation and specific values for diagrams were calculated in Feynman representation using sector decomposition method. Presented approach allows easy automation and generalization for the case of complex symmetries. Also a summation of the perturbation series was obtained by Borel transformation with conformal mapping. The contribution of the 6-th term of the series led to the increase of the Fisher exponent in $O(1)$ model up to $8\\%$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-07T00:55:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponent",
      "fisher exponent",
      "renormalization group approach",
      "sector decomposition method",
      "borel transformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160202324A"
    }
  }
}