{
  "id": "cond-mat/9809315",
  "version": "v3",
  "published": "1998-09-23T16:22:21.000Z",
  "updated": "2000-01-24T13:36:21.000Z",
  "title": "Casimir amplitudes in a quantum spherical model with long-range interaction",
  "authors": [
    "H. Chamati",
    "D. M. Danchev",
    "N. S. Tonchev"
  ],
  "comment": "10 pages latex, no figures, to appear in EPJB (2000)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "A $d$-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size $L$ and ``temporal size'' $1/T $ ($T$ - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions $\\frac 12\\sigma <d<\\frac 32\\sigma $, where $0<\\sigma \\leq 2$ is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if $d=\\sigma$, the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is $\\Delta =-16\\zeta(3)/[5\\sigma(4\\pi)^{\\sigma/2}\\Gamma (\\sigma /2)]$. The last implies that the universal constant $\\tilde{c}=4/5$ of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that $\\tilde{c}=1$. This is a generalization to the case of long-range interaction of the well known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for $d=\\sigma=1$ is $\\tilde c=0.606$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-01-24T13:36:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-range interaction",
      "casimir amplitude",
      "quantum spherical model",
      "temperature",
      "periodic boundary conditions"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998cond.mat..9315C"
    }
  }
}