Localization in Two Dimensions, Gaussian Field Theories, and Multifractality
- 11 November 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 77 (20) , 4194-4197
- https://doi.org/10.1103/physrevlett.77.4194
Abstract
We calculate nonperturbatively the multifractal scaling exponents of the critical wave function for two dimensional Dirac fermions in the presence of a random magnetic field. We do so by arguing that the multifractal scaling exponents can be expressed in terms of the free energy of random directed polymers on a Cayley tree. We find a weak-strong disorder transition for the multifractal scaling exponents of the wave function that is parallel to the freezing or glassy transition of the random polymer model.Keywords
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This publication has 12 references indexed in Scilit:
- Liouville Theory as a Model for Prelocalized States in Disordered ConductorsPhysical Review Letters, 1996
- Two-dimensional conformal field theory for disordered systems at criticalityNuclear Physics B, 1996
- Integer quantum Hall transition: An alternative approach and exact resultsPhysical Review B, 1994
- Localized states in ad-wave superconductorPhysical Review Letters, 1993
- Instability of the fixed point of theO(N) nonlinear σ-model in (2+ε) dimensionsPhysical Review Letters, 1993
- ELECTRONIC SPECTRAL AND WAVEFUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASIPERIODIC SYSTEMS: A SCALING APPROACHInternational Journal of Modern Physics B, 1992
- Solution of the generalised random energy modelJournal of Physics C: Solid State Physics, 1986
- Critical behavior of disordered degenerate semiconductors. I. Models, symmetries, and formalismPhysical Review B, 1986
- Random-energy model: An exactly solvable model of disordered systemsPhysical Review B, 1981
- Ground state of a spin-½ charged particle in a two-dimensional magnetic fieldPhysical Review A, 1979