Anomalous acoustic behaviour and backbone structure of percolation clusters

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Abstract
A real-space renormalisation group method is used to investigate acoustic properties of percolation lattices in the vicinity of the percolation threshold. Scaling form an expressions for critical exponents x, y describing the sound velocity are derived. The existence of an anomalous dispersion relation is elucidated. Dimensionalities dT and dL which represent the geometrical structure of cluster backbones are introduced. The exponents x, y and the dimensionalities dT, dL are expressed in terms of other exponents nu , beta , t, s and beta B for percolation and their explicit values are evaluated from known estimates for nu , beta , t, s and beta B. A geometrical picture of the backbone structure is obtained in terms of the dimensionalities.

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