Abstract
Three-, two-, and one-dimensional disordered systems with randomly distributed, purely repulsive scattering centers, known as Lorentz models, are studied in the low energy limit [1]. Using a functional integral representation and a version of the “replica trick”, we have found in the
D-dimensional system the density of electronic levels of the form
n(E)=b
0Eγ
exp(−b
1E
−(
D
2
)
+b
2E
−(
D
2
)+1
+·+b
DE
−(
1
2
)
)(1+O(
E
))
and the constants
b
0,
b
1,…,
b
D
, and γ have been determined.