{
  "id": "0710.4436",
  "version": "v2",
  "published": "2007-10-24T11:58:46.000Z",
  "updated": "2008-03-14T13:57:31.000Z",
  "title": "Thermodynamic Casimir effects involving interacting field theories with zero modes",
  "authors": [
    "Daniel Grüneberg",
    "H. W. Diehl"
  ],
  "comment": "23 pages, 10 figures",
  "journal": "Phys. Rev. B 77, 115409 (2008)",
  "doi": "10.1103/PhysRevB.77.115409",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\\to\\infty$. The effective forces induced by thermal fluctuations at and above the bulk critical temperature $T_{c,\\infty}$ (thermodynamic Casimir effect) are investigated below the upper critical dimension $d^*=4$ by means of field-theoretic renormalization group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [\\textit{Europhys. Lett.} \\textbf{75}, 241 (2006)], the zero modes that are present in Landau theory at $T_{c,\\infty}$ make conventional RG-improved perturbation theory in $4-\\epsilon$ dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures $T\\geqT_{c,\\infty}$ as functions of $\\mathsf{L}\\equiv L/\\xi_\\infty$, where $\\xi_\\infty$ is the bulk correlation length. Scaling functions of the $L$-dependent residual free energy per area are obtained whose $\\mathsf{L}\\to0$ limits are in conformity with previous results for the Casimir amplitudes $\\Delta_C$ to $O(\\epsilon^{3/2})$ and display a more reasonable small-$\\mathsf{L}$ behavior inasmuch as they approach the critical value $\\Delta_C$ monotonically as $\\mathsf{L}\\to 0$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-03-14T13:57:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "68.15.+e",
      "75.40.-s",
      "68.35.Rh",
      "05.70.Jk",
      "11.10.Hi"
    ],
    "keywords": [
      "thermodynamic casimir effect",
      "interacting field theories",
      "zero modes",
      "field-theoretic renormalization group methods",
      "dependent residual free energy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2008,
      "month": "Mar",
      "volume": 77,
      "number": 11,
      "pages": 115409
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 765314,
      "adsabs": "2008PhRvB..77k5409G"
    }
  }
}