{
  "id": "1410.5296",
  "version": "v1",
  "published": "2014-10-20T14:42:07.000Z",
  "updated": "2014-10-20T14:42:07.000Z",
  "title": "Finite-size scaling above the upper critical dimension",
  "authors": [
    "Matthew Wittmann",
    "A. P. Young"
  ],
  "comment": "11 pages, 15 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of hyperscaling due to a dangerous irrelevant variable, applies only to k=0 fluctuations, and so there is only a single exponent eta describing power-law decay of correlations at criticality, in contrast to recent claims. With free boundary conditions the finite-size \"shift\" is greater than the rounding. Nonetheless, using T-T_L, where T_L is the finite-size pseudocritical temperature, rather than T-T_c, as the scaling variable, the data does collapse on to a scaling form which includes the behavior both at T_L, where the susceptibility chi diverges like L^{d/2} and at the bulk T_c where it diverges like L^2. These claims are supported by large-scale simulations on the 5-dimensional Ising model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-20T14:42:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.50.+q",
      "05.70.Jk",
      "64.60.an",
      "64.60.F-"
    ],
    "keywords": [
      "upper critical dimension",
      "finite-size scaling",
      "single exponent eta describing power-law",
      "exponent eta describing power-law decay",
      "free boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.90.062137",
      "journal": "Physical Review E",
      "year": 2014,
      "month": "Dec",
      "volume": 90,
      "number": 6,
      "pages": "062137"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvE..90f2137W"
    }
  }
}