{
  "id": "1405.5787",
  "version": "v2",
  "published": "2014-05-22T15:10:44.000Z",
  "updated": "2014-12-10T15:24:01.000Z",
  "title": "Comment on \"Casimir force in the $O(n\\to\\infty)$ model with free boundary conditions\"",
  "authors": [
    "H. W. Diehl",
    "Daniel Grüneberg",
    "Martin Hasenbusch",
    "Alfred Hucht",
    "Sergei B. Rutkevich",
    "Felix M. Schmidt"
  ],
  "comment": "Comment on arXiv:1210.1452, see also arXiv:1402.3510, accepted",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "In a recent paper [D. Dantchev, J. Bergnoff, and J. Rudnick, Phys. Rev. E 89, 042116 (2014)] the problem of the Casimir force in the $O(n)$ model on a slab with free boundary conditions, investigated earlier by us [EPL 100, 10004 (2012)], is reconsidered using a mean spherical model with separate constraints for each layer. The authors (i) question the applicability of the Ginzburg-Landau-Wilson approach to the low-temperature regime, arguing for the superiority of their model compared to the family of $\\phi^4$ models A and B whose numerically exact solutions we determined both for values of the coupling constant $0<g<\\infty$ and $g=\\infty$. They (ii) report consistency of their results with ours in the critical region and a strong manifestation of universality, but (iii) point out discrepancies with our results in the region below $T_{\\mathrm{c}}$. We show here that (i) is unjustified and prove that our model B with $g=\\infty$ is identical to their spherical model. Hence evidence for the reported universality is already contained in our work. Moreover, the results we determined for anyone of the models A and B for various thicknesses $L$ are all numerically exact. (iii) is due to their misinterpretation of our results for the scaling limit. We also show that their low-temperature expansion, which does not hold inside the scaling regime, is limited to temperatures lower than they anticipated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-22T15:10:44.000Z",
      "comment": "Comment on arXiv:1210.1452, see also arXiv:1402.3510",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-10T15:24:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "64.60.F-",
      "75.40.-s"
    ],
    "keywords": [
      "free boundary conditions",
      "casimir force",
      "low-temperature regime",
      "mean spherical model",
      "temperatures lower"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.91.026101",
      "journal": "Physical Review E",
      "year": 2015,
      "month": "Feb",
      "volume": 91,
      "number": 2,
      "pages": "026101"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhRvE..91b6101D"
    }
  }
}