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Transport on Directed Percolation Clusters

Hans-Karl Janssen·Olaf Stenull
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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 $ϕ$ 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.

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Hans-Karl Janssen, Olaf Stenull. 2001-03-13. Transport on Directed Percolation Clusters. https://doi.org/10.1103/physreve.63.025103

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