Critical generalized inverse participation ratio distributions
E. Cuevas
Abstract
The system size dependence of the fluctuations in generalized inverse participation ratios (IPR's) Iα(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 q2 according to theoretical estimates. These results ensure the self-averaging of the corresponding generalized dimensions.
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