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We study nonlinear random resistor diode networks at the transition from thenon percolating to the directed percolating phase. The resistor-like bonds andthe 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 afield theoretic model. We focus on the average two-port resistance, which isgoverned at the transition by the resistance exponent $\phi_r$. By employingrenormalization group methods we calculate $\phi_r$ for arbitrary $r$ toone-loop order. Then we address the fractal dimensions characterizing directedpercolation clusters. Via considering distinct values of the nonlinearity $r$,we determine the dimension of the red bonds, the chemical path and the backboneto two-loop order.Comment: 18 pages, 3 figures, minor change

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