Finite-size scaling of correlation functions in finite systems

Xin Zhang, Gao Ke Hu, Yong Wen Zhang, Xiao Teng Li, Xiao Song Chen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish
Article number120511
JournalScience China: Physics, Mechanics and Astronomy
Volume61
Issue number12
DOIs
StatePublished - 1 Dec 2018
Externally publishedYes

Keywords

  • correlation function
  • critical phenomena
  • finite-size scaling
  • lattice model

ASJC Scopus subject areas

  • Physics and Astronomy (all)

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