Finite-size scaling of correlation functions in finite systems

查看全文 作　　者：Xin [1,3]Zhang;GaoKe [1,3]Hu;YongWen [1,2]Zhang;XiaoTeng [1,3]Li;XiaoSong [1,3]Chen 机构地区：[1]Institute of Theoretical Physics,Key Laboratory of Theoretical Physics,Chinese Academy of Sciences,Beijing 100190,China;[2]Data Science Research Center,Kunming University of Science and Technology,Kanming 100190,China;[3]School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China 出　　处：《Science China(Physics,Mechanics & Astronomy)》索引2018年第61卷第12期,共7页 基　　金：supported by the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZD-SSW-SYS019);received a postdoctoral fellowship funded by the KunmingUniversity of Science and Technology 摘　　要：We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional 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 tL^(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis 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 exponentη. 关 键 词：CRITICAL PHENOMENA FINITE-SIZE SCALING CORRELATION function LATTICE model