{
  "id": "cond-mat/9903103",
  "version": "v1",
  "published": "1999-03-05T18:20:23.000Z",
  "updated": "1999-03-05T18:20:23.000Z",
  "title": "Violation of Finite-Size Scaling in Three Dimensions",
  "authors": [
    "X. S. Chen",
    "V. Dohm"
  ],
  "comment": "LaTex, 51 pages",
  "doi": "10.1007/s100510050901",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We reexamine the range of validity of finite-size scaling in the $\\phi^4$ lattice model and the $\\phi^4$ field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the $\\phi^4$ theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size $L$ with periodic boundary conditions we analyze the approach towards bulk critical behavior as $L \\to \\infty$ at fixed $\\xi$ for $T > T_c$ where $\\xi$ is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the $\\phi^4$ lattice model and the $\\phi^4$ field theory in the region $L \\gg \\xi$. The non-scaling effects in the field theory and in the lattice model differ significantly from each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-03-05T18:20:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Jk",
      "64.60.-i"
    ],
    "keywords": [
      "finite-size scaling",
      "field theory",
      "dimensions",
      "analysis ordinary renormalized perturbation theory",
      "bulk correlation length"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "European Physical Journal B",
      "year": 1999,
      "month": "Aug",
      "volume": 10,
      "number": 4,
      "pages": 687
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 497050,
      "adsabs": "1999EPJB...10..687C"
    }
  }
}