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

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

2002-05-17

arxiv.org/abs/cond-mat/0205375v1

Phys. Rev. B 66, 094201 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures

Scientific paper

10.1103/PhysRevB.66.094201

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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