{
  "id": "1702.05072",
  "version": "v1",
  "published": "2017-02-16T18:25:26.000Z",
  "updated": "2017-02-16T18:25:26.000Z",
  "title": "Revisiting (logarithmic) scaling relations using renormalization group",
  "authors": [
    "J. J. Ruiz-Lorenzo"
  ],
  "comment": "9 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "We compute explicitly the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper critical behavior (for short and long range $\\phi^n$-theories) and below it. This allows us to check the scaling relations among these critical exponents obtained by analysing the complex singularities (Lee-Yang and Fisher zeroes) of these models. Moreover, we have obtained an explicit method to compute the $\\hat{\\qq}$ exponent (defined by $\\xi\\sim L (\\log L)^{\\hat{\\qq}}$) and, finally, we have found a new derivation of the scaling law associated with it.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-16T18:25:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scaling relations",
      "mean field behavior",
      "renormalization group equations",
      "critical exponents",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}