RPA-CPA theory for magnetism in disordered Heisenberg binary systems   with long range exchange integrals
  We present a theory based on Green's function formalism to study magnetism in disordered Heisenberg systems with long range exchange integrals. Disordered Green's function are decoupled within Tyablicov scheme and solved with a CPA method. The CPA method is the extension of Blackmann-Esterling-Beck approach to system with environmental disorder term which uses cumulant summation of the single-site non crossing diagrams. The crucial point is that we are able to treat simultaneously and self-consistently the RPA and CPA loops. It is shown that the summation of s-scattering contribution can always be performed analytically. While the p,d,f .. contributions are difficult to handle in the case of long-range coupling. To overcome this difficulty we propose and provide a test of a simplified treatment of these terms. In the case of 3D disordered nearest-neighbor Heisenberg system, a good agreement between the simplified treatment and the full calculation is achieved. Our theory allows in particular to calculate the Curie temperature, the spectral functions and the temperature dependence of the magnetization of each constituant as a function of concentration of impurity. Additionally it is shown that a virtual crystal treatment fails even at low impurity concentration 
G. Bouzerar and P. Bruno