Anomalously large critical regions in power-law random matrix ensembles
Disordered Systems and Neural Networks
2009-10-31 v2
Abstract
We investigate numerically the power-law random matrix ensembles. Wavefunctions 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.
Keywords
Cite
@article{arxiv.cond-mat/0011428,
title = {Anomalously large critical regions in power-law random matrix ensembles},
author = {E. Cuevas and V. Gasparian and M. Ortuno},
journal= {arXiv preprint arXiv:cond-mat/0011428},
year = {2009}
}
Comments
RevTex, 4 pages, 4 eps figures. Final version to be published in Phys. Rev. Lett