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Critical generalized inverse participation ratio distributions

E. Cuevas
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Abstract

The system size dependence of the fluctuations in generalized inverse participation ratios (IPR's) $I_α(q)$ 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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E. Cuevas. 2002-12-11. Critical generalized inverse participation ratio distributions. https://doi.org/10.1103/physrevb.66.233103

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