scholarly journals SCALING THEORY OF ANDERSON LOCALIZATION IN DISORDERED SYSTEMS WITH SPACE MODULATIONS A REAL SPACE RENORMALIZATION GROUP APPROACH

1985 ◽  
Vol 34 (12) ◽  
pp. 1530
Author(s):  
XIONG SHI-JIE ◽  
CAI JIAN-HUA
Keyword(s):  
Renormalization Group ◽  
Disordered Systems ◽  
Anderson Localization ◽  
Real Space ◽  
Scaling Theory ◽  
Group Approach ◽  
Real Space Renormalization Group ◽  
Renormalization Group Approach

scholarly journals INHOMOGENEOUS FIXED POINT ENSEMBLES REVISITED

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1811-1822 ◽  
Author(s):  
Franz J. Wegner
Keyword(s):  
Fixed Point ◽  
Density Of States ◽  
Disordered Systems ◽  
Scaling Law ◽  
Localization Length ◽  
Power Laws ◽  
Real Space ◽  
Group Approach ◽  
Real Space Renormalization Group ◽  
Renormalization Group Approach

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.

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