Abstract
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 are nonfluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between and the spectral compressibility is violated in the regime of strong multifractality, with in the limit .
- Received 10 January 2000
DOI:https://doi.org/10.1103/PhysRevLett.84.3690
©2000 American Physical Society