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 >> 1 for the model of D-component classical spin vectors in the limit D --> infinity, 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 three to two dimensions in magnetic films. In the spatially inhomogeneous case with free boundary conditions the D = infinity model is non-equivalent to the standard spherical one and always leads to the diminishing of T-c(N) relative to the bulk.