Susceptibility scaling functions for ferromagnetic Ising films

The susceptibility of simple-cubic-lattice ferromagnetic Ising films of $n$ two-dimensional lattice layers is studied by extrapolation of high-temperature series expansions (to eleventh and twelfth orders) for $n=3,4,\dots ,14\mathrm{}$ layers with periodic boundary conditions, and $n=3,4,\dots ,10\mathrm{}$ layers with free-surface conditions. The corresponding surface susceptibility series for sc, bcc, and fcc lattices are analyzed in the light of universality hypotheses. On the basis of finite-size scaling theory explicit scaling functions are constructed describing the crossover from two-dimensional to three-dimensional critical behavior in terms of the ratio $\frac{n}{\xi \mathrm{}\left(T\right)\mathrm{}}$, where $\xi \sim \Delta T^{-\nu }$ is the bulk correlation length.