2 research outputs found
On the Finite Size Scaling in Disordered Systems
The critical behavior of a quenched random hypercubic sample of linear size
is considered, within the ``random-'' field-theoretical mode, by
using the renormalization group method. A finite-size scaling behavior is
established and analyzed near the upper critical dimension and
some universal results are obtained. The problem of self-averaging is clarified
for different critical regimes.Comment: 21 pages, 2 figures, submitted to the Physcal Review
Edge state transmission, duality relation and its implication to measurements
The duality in the Chalker-Coddington network model is examined. We are able
to write down a duality relation for the edge state transmission coefficient,
but only for a specific symmetric Hall geometry. Looking for broader
implication of the duality, we calculate the transmission coefficient in
terms of the conductivity and in the diffusive
limit. The edge state scattering problem is reduced to solving the diffusion
equation with two boundary conditions
and
.
We find that the resistances in the geometry considered are not necessarily
measures of the resistivity and () holds only
when is quantized. We conclude that duality alone is not sufficient
to explain the experimental findings of Shahar et al and that Landauer-Buttiker
argument does not render the additional condition, contrary to previous
expectation.Comment: 16 pages, 3 figures, to appear in Phys. Rev.