{
  "id": "1209.4650",
  "version": "v2",
  "published": "2012-09-20T20:00:25.000Z",
  "updated": "2012-12-11T09:30:38.000Z",
  "title": "Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions",
  "authors": [
    "Thomas Kloss",
    "Léonie Canet",
    "Nicolás Wschebor"
  ],
  "comment": "21 pages, 7 figures, minor corrections prior to publication",
  "journal": "Phys. Rev. E 86, 051124 (2012)",
  "doi": "10.1103/PhysRevE.86.051124",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We investigate the strong-coupling regime of the stationary Kardar-Parisi-Zhang equation for interfaces growing on a substrate of dimension d=1, 2, and 3 using a nonperturbative renormalization group (NPRG) approach. We compute critical exponents, correlation and response functions, extract the related scaling functions and calculate universal amplitude ratios. We work with a simplified implementation of the second-order (in the response field) approximation proposed in a previous work [PRE 84, 061128 (2011) and Erratum 86, 019904 (2012)], which greatly simplifies the frequency sector of the NPRG flow equations, while keeping a nontrivial frequency dependence for the 2-point functions. The one-dimensional scaling function obtained within this approach compares very accurately with the scaling function obtained from the full second-order NPRG equations and with the exact scaling function. Furthermore, the approach is easily applicable to higher dimensions and we provide scaling functions and amplitude ratios in d=2 and d=3. We argue that our ansatz is reliable up to d \\simeq 3.5.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-12-11T09:30:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.Ht",
      "68.35.Ct",
      "05.10.-a",
      "68.35.Rh"
    ],
    "keywords": [
      "scaling function",
      "stationary kardar-parisi-zhang equation",
      "nonperturbative renormalization group",
      "full second-order nprg equations",
      "universal amplitude ratios"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2012,
      "month": "Nov",
      "volume": 86,
      "number": 5,
      "pages": "051124"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1187639,
      "adsabs": "2012PhRvE..86e1124K"
    }
  }
}