INHOMOGENEOUS FIXED POINT ENSEMBLES REVISITED

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 µ = dν-1 was derived for the power laws of the density of states ρ ∝ |E|µ and of the localization length ξ ∝ |E|-ν. This prediction from 1976 is checked against explicit results obtained meanwhile.