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Nonlinear random resistor diode networks and fractal dimensions of directed percolation clusters

Olaf Stenull·Hans-Karl Janssen
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Abstract

We study nonlinear random resistor diode networks at the transition from the non percolating to the directed percolating phase. The resistor-like bonds and the diode-like bonds under forward bias voltage obey a generalized Ohm's law, $V \sim I^r$. Based on general grounds as symmetries and relevance we develop a field theoretic model. We focus on the average two-port resistance, which is governed at the transition by the resistance exponent $ϕ_r$. By employing renormalization group methods we calculate $ϕ_r$ for arbitrary $r$ to one-loop order. Then we address the fractal dimensions characterizing directed percolation clusters. Via considering distinct values of the nonlinearity $r$, we determine the dimension of the red bonds, the chemical path and the backbone to two-loop order.

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Olaf Stenull, Hans-Karl Janssen. 2001-07-06. Nonlinear random resistor diode networks and fractal dimensions of directed percolation clusters. https://doi.org/10.1103/physreve.64.016135

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