Multifractal properties of resistor diode percolation

Abstract

Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the non-percolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are governed by a family of critical exponents $\{{\psi }_l\}$. We calculate the family $\{{\psi }_l\}$ to two-loop order in a diagrammatic perturbation calculation augmented by renormalization group methods.

21 pages, 5 figures, to appear in Phys. Rev. E

References in corpus (7)

• Behavioral-Independent Features of Complex Heartbeat Dynamics
• Conductivity of continuum percolating systems
• Nonlinear random resistor diode networks and fractal dimensions of directed percolation clusters
• On the relevance of percolation theory to the vulcanization transition
• Multifractality in directed percolation
• Effects of surfaces on resistor percolation
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