Phys. Rev. Lett. 84, 3690–3693 (2000)Fluctuations of the Inverse Participation Ratio at the Anderson TransitionReceived 10 January 2000; published in the issue dated 17 April 2000 Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale invariant, with a power-law asymptotic “tail.” This scale invariance implies that the fractal dimensions Dq are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between D2 and the spectral compressibility χ is violated in the regime of strong multifractality, with χ→1 in the limit D2→0. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.84.3690
DOI:
10.1103/PhysRevLett.84.3690
PACS:
72.15.Rn, 05.40.-a, 05.45.Df, 71.30.+h
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