Fractal effects on excitations in dilute ferromagnets

The long-wavelength spin-wave excitations in dilute ferromagnets are studied. With the use of a fractal model for the backbone of the infinite percolating cluster of Kirkpatrick, a new relation is obtained between the percolation exponents and the exponent characterizing the vanishing of spin-wave stiffness. This also enables us to express the conductivity exponent in terms of various percolation exponents. For dilute magnets the importance of fractal effects in the calculation of density of states and the low-temperature thermodynamics is pointed out.