Abstract
We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes in terms of the chemical (minimal) path, we show theoretically that the ψ’s are characterized by a logarithmically broad distribution, and display multifractal features as a function of the Euclidean distance. The moments of exhibit novel crossover phenomena. Our numerical simulations of fractons exhibit a nontrivial distribution of localization lengths, even when the chemical distance is fixed. These results are explained via a generalization of the theory.
- Received 28 July 1992
DOI:https://doi.org/10.1103/PhysRevLett.69.3189
©1992 American Physical Society