Anomalously large critical regions in power-law random matrix ensembles - art. no. 056601

We investigate numerically the power-law random matrix ensembles. Wave func tions are fractal up to a characteristic length whose logarithm diverges as ymmetrically with different exponents, I in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which thi s length is larger than the system size. The Green's functions decrease wit h distance as a power law with an exponent related to the correlation dimen sion.