Susceptibilities and correlation functions of the anisotropic spherical model

The static transverse and longitudinal correlation functions (CF) of a 3-dimensional ferromagnet are calculated for the exactly solvable anisotropic spherical model (ASM) determined as the limit D --> infinity of the classical D-component vector model. The results are nonequivalent to those for the standard spherical model of Berlin and Kac even in the isotropic case. Whereas the transverse CF has the usual Ornstein-Zernike form for small wave vectors, the longitudinal CF shows a nontrivial behavior in the ordered region caused by spin-wave fluctuations. In particular, in the isotropic case below T-c one has S-zz(k) proportional to 1/k (the result of the spin-wave theory) for k less than or similar to kappa(m) proportional to T-c - T.