Finite-size scaling of correlation functions in finite systems

• 来源期刊: 中国科学:物理学 力学 天文学（英文版）
• 年，卷（期）: 2018,（12）
• 页码范围: 67-73
• 页数: 7页
• 语种: 英文

摘要

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a d-dimensional finite system of size L,the correlation function can be written as the product of |r|-(d-2+η) and a finite-size scaling function of the variables r/L and tL1/v,where t =(T-Tc)/Tc,η is the critical exponent of correlation function,and v is the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when |r| is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponent η.