Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field
The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potentia...
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Veröffentlicht in: | arXiv.org 1997-10 |
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Hauptverfasser: | , , , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a Generalized Random Energy Model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.9706084 |