We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes ψi 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 ψi 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. © 1992 The American Physical Society.
Bunde, A., Roman, H., Russ, S., Aharony, A., Harris, A. (1992). Vibrational excitations in percolation: Localization and multifractality. PHYSICAL REVIEW LETTERS, 69(22), 3189-3192 [10.1103/PhysRevLett.69.3189].
Vibrational excitations in percolation: Localization and multifractality
Roman H. E.;
1992
Abstract
We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes ψi 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 ψi 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. © 1992 The American Physical Society.
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