Universal scaling form of the correlation length in Ising strips with periodic, free, fixed, and mixed boundary conditions

According to finite-size scaling theory, the correlation length in an Ising strip with infinite length and a width of L lattice constants has the form ${\xi }_L$(T)=Lf(c(T-$T_c$)L) in the scaling regime L≫1,‖T-$T_c$‖/$T_c$≪1. Here f(x) is a universal scaling function, which does, however, depend on the boundary conditions at the edges of the strip. Utilizing the correspondence between the two-dimensional Ising model and the one-dimensional quantum Ising model in a transverse field, we calculate the explicit form of the function f(x) for spin-spin and energy-energy correlations in strips with periodic, free, fixed, and mixed free-fixed boundary conditions.