Finite- Size Scaling of Correlation Function

• DOI: 10.48550/arxiv.1805.08607
• Publication Date: 2018-01-01
• Authors: Xin Zhang; Gaoke Hu; Yongwen Zhang; Xiaoteng Li; Xiaosong Chen
• Keywords: Exponent; Critical point (mathematics); Percolation (cognitive psychology)

We propose the finite-size scaling of correlation function in a finite system near its critical point. At distance ${\bf r}$ with size $L$, can be written as product $|{\bf r}|^{-(d-2+η)}$ and variables r}/L$ $tL^{1/ν}$, where $t=(T-T_c)/T_c$. The directional dependence is nonnegligible only when r}|$ becomes compariable $L$. This has been confirmed by functions Ising model bond percolation two-diemnional lattices, which are calculated Monte Carlo simulation. use to determine point exponent $η$.