Random network models and quantum phase transitions in two dimensions

@article{Kramer2004RandomNM,
  title={Random network models and quantum phase transitions in two dimensions},
  author={Bernhard K. Kramer and Tomi Ohtsuki and Stefan Kettemann},
  journal={Physics Reports},
  year={2004},
  volume={417},
  pages={211-342}
}
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References

SHOWING 1-10 OF 817 REFERENCES
Two-dimensional random-bond Ising model, free fermions, and the network model
We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions.
MODELING DISORDERED QUANTUM SYSTEMS WITH DYNAMICAL NETWORKS
It is the purpose of the present article to show that so-called network models, originally designed to describe static properties of disordered electronic systems, can be easily generalized to
Quantum and classical localization, the spin quantum Hall effect, and generalizations
We consider network models for localization problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet
Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model
An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N=1 is known to describe the critical behavior at the plateau transition in systems exhibiting
Network models for localization problems belonging to the chiral symmetry classes
We consider localization problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behavior at a band center. We formulate models that have the
Scaling and crossover functions for the conductance in the directed network model of edge states
We consider the directed network (DN) of edge states on the surface of a cylinder of length L and circumference C .B y mapping it to a ferromagnetic superspin chain, and using a scaling analysis, we
Point-contact conductances at the quantum Hall transition
On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the
Connecting polymers to the quantum Hall plateau transition
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau
Random-matrix theory of quantum transport
This is a review of the statistical properties of the scattering matrix of a mesoscopic system. Two geometries are contrasted: A quantum dot and a disordered wire. The quantum dot is a confined
Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma
...
1
2
3
4
5
...