Multiscaling in multifractals

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Abstract
Multiscaling is shown to be a consequence of multifractality when a lower cutoff ɛ is introduced in calculations of correlation functions. After a suitable rescaling, the correlation function data for different values of ɛ seem to fall onto a single curve. In the multiscaling regime, however, we show that there is not a unique functional form at varying ɛ, but a spread very close to a single curve. For each ɛ, this curve can be computed analytically in terms of the f(α) spectrum which characterizes the multifractal. Part of this spectrum can thus be obtained by computing only one moment of the weights at ɛ≠0.