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Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition

I. Varga
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Abstract

The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as the system size is varied exactly at a value obtained from the scaling properties of the typical value of the inverse participation number. Therefore the state-to-state fluctuation of the correlation dimension is tightly linked to the scaling properties of the joint probability distribution of the eigenstates.

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I. Varga. 2002-05-17. Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition. https://doi.org/10.1103/physrevb.66.094201

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