{
  "id": "1401.1357",
  "version": "v2",
  "published": "2014-01-07T12:32:27.000Z",
  "updated": "2014-03-27T10:58:07.000Z",
  "title": "The O(n) $φ^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections",
  "authors": [
    "H. W. Diehl",
    "S. B. Rutkevich"
  ],
  "comment": "published version, some misprints corrected",
  "journal": "Journal of Physics A: Mathematical and Theoretical 47, 145004 (2014)",
  "doi": "10.1088/1751-8113/47/14/145004",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "The $O(n)$ ${\\phi}^4$ model on a slab $\\mathbb{R}^{d-1}\\times[0,L]$ bounded by free surfaces is studied for $2<d<4$ in the limit $n\\to\\infty$. The self-consistent potential $V(z)$ which the exact $n\\to\\infty$ solution of the model involves is analysed by means of boundary operator expansions. Building on the known exact $n\\to\\infty$ solution for $V(z)$ in the semi-infinite case $L=\\infty$ at the bulk critical point, we exactly determine two types of corrections to this potential: (i) those linear in the temperature scaling field $t$ at $L=\\infty$, and (ii) the leading $L$-dependent (distant-wall) corrections at the critical point. From (i) exact analytical results at $d=3$ are obtained for the leading temperature singularity of the excess surface free energy and the implied asymptotic behaviours of the scaling functions $\\Theta_3(x)$ and $\\vartheta_3(x)$ of the residual free energy $f_{\\rm res} =L^{1-d}\\,\\Theta_d(tL)$ and the critical Casimir force $\\beta\\mathcal{F}_{\\rm C}(T,L)=L^{-d}\\,\\vartheta_d(tL)$ in the limit $x\\to 0\\pm$. The second derivative $\\vartheta_3''(0)$ is computed exactly.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-27T10:58:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary critical behaviour",
      "free surfaces",
      "exact results",
      "distant-wall corrections",
      "fluctuation-induced forces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2014,
      "month": "Apr",
      "volume": 47,
      "number": 14,
      "pages": 145004
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1281706,
      "adsabs": "2014JPhA...47n5004D"
    }
  }
}