{
  "id": "cond-mat/0402238",
  "version": "v1",
  "published": "2004-02-09T15:00:51.000Z",
  "updated": "2004-02-09T15:00:51.000Z",
  "title": "The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results",
  "authors": [
    "Daniel Dantchev",
    "Michael Krech"
  ],
  "comment": "21 pages, 7 figures, to appear in PRE",
  "journal": "Phys.Rev. E69 (2004) 046119",
  "doi": "10.1103/PhysRevE.69.046119",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present general arguments and construct a stress tensor operator for finite lattice spin models. The average value of this operator gives the Casimir force of the system close to the bulk critical temperature $T_c$. We verify our arguments via exact results for the force in the two-dimensional Ising model, $d$-dimensional Gaussian and mean spherical model with $2<d<4$. On the basis of these exact results and by Monte Carlo simulations for three-dimensional Ising, XY and Heisenberg models we demonstrate that the standard deviation of the Casimir force $F_C$ in a slab geometry confining a critical substance in-between is $k_b T D(T)(A/a^{d-1})^{1/2}$, where $A$ is the surface area of the plates, $a$ is the lattice spacing and $D(T)$ is a slowly varying nonuniversal function of the temperature $T$. The numerical calculations demonstrate that at the critical temperature $T_c$ the force possesses a Gaussian distribution centered at the mean value of the force $<F_C>=k_b T_c (d-1)\\Delta/(L/a)^{d}$, where $L$ is the distance between the plates and $\\Delta$ is the (universal) Casimir amplitude.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-09T15:00:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monte carlo results",
      "critical casimir force",
      "finite lattice spin models",
      "exact results",
      "fluctuations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 644202
    }
  }
}