Critical generalized inverse participation ratio distributions

Abstract

The system size dependence of the fluctuations in generalized inverse participation ratios (IPR's) $I_{\alpha }(q)$ at criticality is investigated numerically. The variances of the IPR logarithms are found to be scale-invariant at the macroscopic limit. The finite size corrections to the variances decay algebraically with nontrivial exponents, which depend on the Hamiltonian symmetry and the dimensionality. The large-$q$ dependence of the asymptotic values of the variances behaves as $q^2$ according to theoretical estimates. These results ensure the self-averaging of the corresponding generalized dimensions.

RevTex4, 5 pages, 4 .eps figures, to be published in Phys. Rev. B

References in corpus (1)

• Fluctuations of the correlation dimension at metal-insulator transitions

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