Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-03-03
Physics
Condensed Matter
Disordered Systems and Neural Networks
Submitted to 'World Scientific' for the volume 'Fifty Years of Anderson Localization'. 12 pages
Scientific paper
The density of states of disordered systems in the Wigner-Dyson classes approaches some finite non-zero value at the mobility edge, whereas the density of states in systems of the chiral and Bogolubov-de Gennes classes shows a divergent or vanishing behavior in the band centre. Such types of behavior were classified as homogeneous and inhomogeneous fixed point ensembles within a real-space renormalization group approach. For the latter ensembles the scaling law $\mu=d\nu-1$ was derived for the power laws of the density of states $\rho\propto|E|^\mu$ and of the localization length $\xi\propto|E|^{-\nu}$. This prediction from 1976 is checked against explicit results obtained meanwhile.
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