LARGE-N LIMIT OF THE HEISENBERG-MODEL - RANDOM EXTERNAL-FIELD AND RANDOM UNIAXIAL ANISOTROPY

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.