Cluster approximation for the Heisenberg ferromagnetic with nonmagnetic impurities

An expression for the stiffness coefficient D of spin waves as a function of impurity concentration was derived for the Heisenberg ferromagnetic substance with nonmagnetic impurities in the limit of low temperatures using a simple cluster method of the Bethe-Peierls type. The pattern of the dependence was shown to change with varying concentration from $D\simeq J_0bSx/2$ at $x\sim 1$ to $D\simeq J_0bS|x—х_0|^{2\tau}$ at $x\sim x_0$.