Magnetic properties of a disordered Heisenberg binary spin system with   long-range exchange
  The influence of substitutional disorder on the magnetic properties of disordered Heisenberg binary spin systems with long-range exchange integrals is studied. The equation of motion for the magnon Green's function which is decoupled by the Tyablikov approximation is solved in the Blackman-Esterling-Berk(BEB) coherent potential approximation(CPA) framework, where the environmental disorder term is treated by virtual crystal approximation. The long-range exchange integrals include a power-law decaying and an oscillating Ruderman-Kittel-Kasuya-Yosida(RKKY) exchange interaction. The resulting spectral density, which is calculated by CPA self-consistent equation, is then used to estimate the magnetization and Curie temperature. The results show, in the case of the three-dimensional simple cubic systems, a strong influence of ferromagnetic long-range exchange integrals on the magnetization and Curie temperature of the systems, which is obviously different from the calculation of short-range interaction. 
G.X. Tang and W. Nolting