Conductivity and spin-wave stiffness in disordered systems-an exactly soluble model

An exact discussion is given of the conductivity of disordered resistor networks and of the related problem of spin-wave stiffness in disordered Heisenberg ferromagnets, by considering the special case of the Bethe lattice. For arbitrary substitutional disorder an exact nonlinear integral equation is obtained for a generating function determining the conductivity and spin-wave stiffness in such branching models. An effective medium (coherent potential) approximation is shown to provide an asymptotically exact solution in the limit of high coordination number z. Its extension, to order (1/z)4, is obtained.