Density of States Exponent for Two-Dimensional Spin-Wave Dynamics at the Percolation Threshold

Numerical techniques are used to obtain the value λ=0.33±0.03 for the exponent characterizing the energy dependence ρ∝E^-λ of the total density of spin-wave states in the diluted two-dimensional Heisenberg ferromagnet at the percolation threshold. The result supports a crossover relationship to static exponents. It is also consistent with a recently calculated dynamic exponent, with current fractal viewpoints and analyses, and with the Alexander-Orbach conjecture.