Fluctuations of the inverse participation ratio at the Anderson transition

F. Evers, A. D. Mirlin

Published 2000-01-08Version 1

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 $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility $\chi$ is violated in the regime of strong multifractality, with $\chi\to 1$ in the limit $D_2\to 0$.