The thermodynamic equivalence of the large-n limit of the n-vector model in a
random external field and the corresponding disordered spherical model is
proved. An analytic expression for the free energy and a phase diagram of the
large-n limit of the n-vector model with random uniaxial anisotropy are
obtained by rigorous argument. The ferromagnetic order in the large-n limit is
proved to be stable against the switching on of an arbitrarily small random
anisotropy.