Spherical Model for Anisotropic Ferromagnetic Films

The corrections to the Curie temperature T_c of a ferromagnetic film consisting of N layers are calculated for N \gg 1 for the model of D-component classical spin vectors in the limit D \to \infty, which is exactly soluble and close to the spherical model. The present approach accounts, however, for the magnetic anisotropy playing the crucial role in the crossover from 3 to 2 dimensions in magnetic films. In the spatially inhomogeneous case with free boundary conditions the D=\infty model is nonequivalent to the standard spherical one and always leads to the diminishing of T_c(N) relative to the bulk.