{
  "id": "1805.08607",
  "version": "v1",
  "published": "2018-05-22T14:25:29.000Z",
  "updated": "2018-05-22T14:25:29.000Z",
  "title": "Finite- Size Scaling of Correlation Function",
  "authors": [
    "Xin Zhang",
    "Gaoke Hu",
    "Yongwen Zhang",
    "Xiaoteng Li",
    "Xiaosong Chen"
  ],
  "comment": "7 pages, 13 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance ${\\bf r}$ in the finite system with size $L$, the correlation function can be written as the product of $|{\\bf r}|^{-(d-2+\\eta)}$ and its finite-size scaling function of variables ${\\bf r}/L$ and $tL^{1/\\nu}$, where $t=(T-T_c)/T_c$. The directional dependence of correlation function is nonnegligible only when $|{\\bf r}|$ becomes compariable with $L$. This finite-size scaling of correlation function has been confirmed by correlation functions of the Ising model and the bond percolation in two-diemnional lattices, which are calculated by Monte Carlo simulation. We can use the finite-size scaling of correlation function to determine the critical point and the critical exponent $\\eta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-22T14:25:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "correlation function",
      "finite-size scaling",
      "finite system",
      "critical point",
      "monte carlo simulation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}