Finite-size scaling of correlation functions in finite systems

  • Xin Zhang
  • GaoKe Hu
  • YongWen Zhang
  • XiaoTeng Li
  • XiaoSong ChenEmail author


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 = (TTc)=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.


critical phenomena finite-size scaling correlation function lattice model 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xin Zhang
    • 1
    • 3
  • GaoKe Hu
    • 1
    • 3
  • YongWen Zhang
    • 1
    • 2
  • XiaoTeng Li
    • 1
    • 3
  • XiaoSong Chen
    • 1
    • 3
    Email author
  1. 1.Institute of Theoretical Physics, Key Laboratory of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  2. 2.Data Science Research CenterKunming University of Science and TechnologyKunmingChina
  3. 3.School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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