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±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, T\"{a}uber, and Schwabl and clear up some minor shortcomings.