Multifractal nature of fractons on a percolating cluster

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Abstract
We show that the amplitude fluctuations of fractons on a percolating cluster have well-defined multifractal properties. The multifractal spectrum turns out to be explicitly dependent on the frequency of the modes and rather stable for modes with similar frequency. The physical implications of this result are that self-similar fluctuations are an intrinsic characteristic of fractons. Therefore, smoothing or averaging procedures can be questionable in this respect. This property could also help clarify the ambiguities that are present in the definition of the correlation length. It is interesting to note that the localization of fractons is of a different nature with respect to Anderson localized wave functions because these are multifractal only at the mobility edge.