Random Resistor-Diode Networks and the Crossover from Isotropic to Directed Percolation

Abstract

By employing the methods of renormalized field theory we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic model from the general epidemic process by including a relevant isotropy-breaking perturbation. We present a two-loop calculation of the crossover exponent $ϕ$. Upon blending the $ε$-expansion result with the exact value $ϕ=1$ for one dimension by a rational approximation, we obtain for two dimensions $ϕ= 1.29\pm 0.05$. This value is in agreement with the recent simulations of a two-dimensional random diode network by Inui, Kakuno, Tretyakov, Komatsu, and Kameoka, who found an order parameter exponent $β$ different from those of isotropic and directed percolation. Furthermore, we reconsider the theory of the full crossover from isotropic to directed percolation by Frey, Täuber, and Schwabl and clear up some minor shortcomings.