English

Finite- Size Scaling of Correlation Function

Statistical Mechanics 2018-06-01 v2

Abstract

We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance r{\bf r} in the finite system with size LL, the correlation function can be written as the product of r(d2+η)|{\bf r}|^{-(d-2+\eta)} and its finite-size scaling function of variables r/L{\bf r}/L and tL1/νtL^{1/\nu}, where t=(TTc)/Tct=(T-T_c)/T_c. The directional dependence of correlation function is nonnegligible only when r|{\bf r}| becomes compariable with LL. 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 η\eta.

Keywords

Cite

@article{arxiv.1805.08607,
  title  = {Finite- Size Scaling of Correlation Function},
  author = {Xin Zhang and Gaoke Hu and Yongwen Zhang and Xiaoteng Li and Xiaosong Chen},
  journal= {arXiv preprint arXiv:1805.08607},
  year   = {2018}
}

Comments

7 pages, 13 figures

R2 v1 2026-06-23T02:04:13.848Z