FRACTION DENSITY OF STATES BY THE MAXIMUM-ENTROPY METHOD

We present a study of the one-magnon density of states in the three-dimensional dilute Heisenberg ferromagnet. The ensemble-averaged density of states is evaluted by calculating a small number of spectral moments and employing a maximum-entropy criterion. Finite-size-lattice data, via common numerical simulation techniques, are also presented. The results demonstrate the fraction excitations at the percolation concentration p(c) as expected from the Alexander-Orbach conjecture and show the presence of the magnon-to-fracton crossover. At the percolation threshold p(c), we estimate a value for the spectral dimension of d(s) almost-equal-to 1.52. The corresponding problem of phonons in random materials is also discussed in connection with the available experimental data.