{
  "id": "cond-mat/9907024",
  "version": "v1",
  "published": "1999-07-02T06:45:14.000Z",
  "updated": "1999-07-02T06:45:14.000Z",
  "title": "The Sixth-Moment Sum Rule For the Pair Correlations of the Two-Dimensional One-Component Plasma: Exact Result",
  "authors": [
    "P. Kalinay",
    "P. Markos",
    "L. Samaj",
    "I. Travenec"
  ],
  "comment": "24 pages",
  "journal": "J. Stat. Phys. 98 (2000) 639",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The system under consideration is a two-dimensional one-component plasma in fluid regime, at density n and at arbitrary coupling Gamma=beta e^2 (e=unit charge, beta = inverse temperature). The Helmholtz free energy of the model, as the generating functional for the direct pair correlation c, is treated in terms of a convergent renormalized Mayer diagrammatic expansion in density. Using specific topological transformations within the bond-renormalized Mayer expansion we prove that the nonzero contributions to the regular part of the Fourier component of c up to the k^2-term originate exclusively from the ring diagrams (unable to undertake the bond-renormalization procedure) of the Helmholtz free energy. In particular, c(k)=-Gamma/k^2 + Gamma/(8 pi n) - k^2/[96(pi n)^2] + O(k^4). This result fixes via the Ornstein-Zernike relation, besides the well-known zeroth-, second- and fourth- moment sum rules, the new six-momnt condition for the truncated pair correlation h, n(pi Gamma n/2)^3 Integral r^6 h(r) d^2 r = 3(Gamma-6)(8-3 Gamma)/4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-02T06:45:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "two-dimensional one-component plasma",
      "pair correlation",
      "sixth-moment sum rule",
      "exact result",
      "helmholtz free energy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999cond.mat..7024K"
    }
  }
}