Critical generalized inverse participation ratio distributions

Details Critical generalized inverse participation ratio distributions Critical generalized inverse participation ratio distributions

2002-04-09

arxiv.org/abs/cond-mat/0204197v2

Phys. Rev. B 66, 233103 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevB.66.233103

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.

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