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Multifractal properties of resistor diode percolation
Olaf Stenull1, Hans-Karl Janssen
1Institut für Theoretische Physik III, Heinrich-Heine-Universität, Universitätsstrasse 1, 40225 Düsseldorf, Germany.
Summary
We studied electric transport in random resistor diode networks near a critical phase transition. Our findings reveal multifractal properties of current distribution governed by critical exponents, calculated using field theory and renormalization group methods.
Area of Science:
- Condensed Matter Physics
- Statistical Physics
Background:
- Understanding electric transport in disordered systems is crucial.
- Phase transitions in random networks exhibit complex behaviors.
Purpose of the Study:
- Investigate multifractal properties of electric transport.
- Analyze networks at the phase transition between nonpercolating and directed percolating states.
Main Methods:
- Derived a field theoretic Hamiltonian based on symmetries and relevance.
- Calculated multifractal moments of current distribution.
- Employed diagrammatic perturbation and renormalization group methods to two-loop order.
Main Results:
- Determined a family of critical exponents [psi(l)] governing multifractality.
- Quantified the multifractal moments of current distribution.
Conclusions:
- The study provides a detailed analysis of electric transport in random resistor diode networks.
- Identified and calculated critical exponents characterizing multifractal behavior at the phase transition.