Critical parameters from generalised multifractal analysis at the Anderson transition

Abstract

We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction amplitudes is sufficient to characterize the transition. In combination with finite-size scaling, this formalism permits the critical parameters to be estimated without the need for conductance or other transport measurements. Applying this method to high-precision data for wavefunction statistics obtained by exact diagonalization of the three-dimensional Anderson model, we estimate the critical exponent $\nu =1.58\pm 0.03$.

5 pages, 3 figures, 2 tables

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• Multifractality can be a universal signature of phase transitions