Exact calculation of multifractal exponents of the critical wave function of Dirac fermions in a random magnetic field

Horacio E. Castillo, Claudio de C. Chamon, Eduardo Fradkin, Paul M. Goldbart, Christopher Mudry

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)10668-10677
Number of pages10
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume56
Issue number16
DOIs
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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