Transport on Directed Percolation Clusters

Abstract

We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\varphi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.

4 pages

References in corpus (3)

• Diluted Networks of Nonlinear Resistors and Fractal Dimensions of Percolation Clusters
• Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation
• Master Operators Govern Multifractality in Percolation

Cited by in corpus (10)

• Conductivity of continuum percolating systems
• Logarithmic Corrections in Directed Percolation
• Nonlinear random resistor diode networks and fractal dimensions of directed percolation clusters
• Multifractal current distribution in random diode networks
• Multifractality in directed percolation
• Multifractal properties of resistor diode percolation
• Renormalized field theory of resistor diode percolation
• Percolating granular superconductors
• Corrections to Scaling in Random Resistor Networks and Diluted Continuous Spin Models near the Percolation Threshold
• Transport properties of directed percolation clusters at the upper critical dimension