Green function theory of random ferromagnets with large exchange anisotropy

Spin 1/2 systems which are coupled with an Ising-like Hamiltonian with fluctuating exchange are discussed by the use of thermodynamic Green functions in four different approximations. The first is equivalent to a local mean field approximation and the second is an approximation to the first in which the local mean field is assumed to be proportional to the overall magnetization and to the sum of the neighboring exchange 'bonds'. The third is also a special case of the first, but the local mean field is approximated in such a way as to be appropriate for the discussion of spin glasses. The fourth is a coherent potential-like approximation (CPA). The second approximation can be shown to imply no reduction of the Curie temperature (T sub(c)) due to exchange fluctuations, while the CPA does result in a lowering of T sub(c) (assuming small fluctuations about an average positive exchange in both cases). However, the CPA that was used is also an approximation to the second method. Hence, even though the CPA does result in a lowering of T sub(c) (which is generally conceded to be correct for the original model), this fact cannot be used as an argument for the validity of the CPA. This calculation thus emphasizes the necessity of critically examining any CPA-like calculation before accepting its predictions as valid