Finite-size scaling of the correlation length in anisotropic systems

The finite-size scaling functions of thermodynamic functions in anisotropic systems have been shown to be dependent on the spatial anisotropy [X.S. Chen and V. Dohm, Phys. Rev. E 70, 056136 (2004)]. Here we extend this study to the correlation length I I of the anisotropic O(n) symmetric phi(4) model in an Ld-1 x infinity cylindric geometry with periodic boundary conditions. We calculate the exact finite-size scaling function of correlation length xi(parallel to) for T >= T-c in 2 < d < 4 dimensions and in the limit n -> infinity. The finite-size scaling function of xi(parallel to) is dependent on a normalized symmetric (d - 1) x (d - 1) matrix defined by the anisotropy matrix of anisotropic systems.