Anomalously large critical regions in power-law random matrix ensembles.
We investigate numerically the power-law random matrix ensembles. Wave functions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 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 this length is larger than the system size. The Green's functions decrease with distance as a power law with an exponent related to the correlation dimension.
Cuevas
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Departamento de Física, Universidad de Murcia, E-30071 Murcia, Spain.
Gasparian
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Ortuño
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