# Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

@article{Read2000AbsenceOA, title={Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states}, author={Nicholas Read and Andreas W. W. Ludwig}, journal={Physical Review B}, year={2000}, volume={63}, pages={024404} }

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 model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in…

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## References

Exactly solved models in statistical mechanics

- Physics
- 1982

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical…