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The static transverse and longitudinal correlation functions (CF) of a3-dimensional ferromagnet are calculated for the exactly solvable anisotropicspherical model (ASM) determined as the limit D \to \infty of the classicalD-component vector model. The results are nonequivalent to those for thestandard spherical model of Berlin and Kac even in the isotropic case. Whereasthe transverse CF has the usual Ornstein-Zernike form for small wave vectors,the longitudinal CF shows a nontrivial behavior in the ordered region caused byspin-wave fluctuations. In particular, in the isotropic case below T_c one hasS_{zz}(k) \propto 1/k (the result of the spin-wave theory) for k \lsim \kappa_m\propto T_c-T.Comment: 6 pages, 4 figure

Susceptibilities and correlation functions of the anisotropic spherical model