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Published on: September 26, 2014
Random resistor-diode networks and the crossover from isotropic to directed percolation
1Institut fur Theoretische Physik III, Heinrich-Heine-Universitat, 40225 Dusseldorf, Germany.
Summary
Random resistor-diode networks near critical points exhibit isotropic percolation behavior. A new model and calculation yield a crossover exponent of 1.29±0.05 in two dimensions, aligning with simulations.
Area of Science:
- Statistical physics
- Complex systems
- Condensed matter theory
Background:
- Percolation theory describes the formation of connected clusters in random systems.
- Random resistor-diode networks exhibit complex behavior near critical points.
- Universality classes categorize systems with similar critical phenomena.
Purpose of the Study:
- To determine the universality class of random resistor-diode networks near the multicritical line.
- To investigate the crossover behavior from isotropic to directed percolation.
- To calculate the crossover exponent using theoretical methods.
Main Methods:
- Renormalized field theory and mesoscopic modeling.
- Incorporation of an isotropy-breaking perturbation into a general epidemic process model.
- Two-loop calculation of the crossover exponent (φ).
- Rational approximation blending ε-expansion with 1D exact values.
Main Results:
- Percolation in random resistor-diode networks belongs to the isotropic percolation universality class.
- A two-loop calculation yields a crossover exponent φ = 1.29±0.05 in two dimensions.
- This result agrees with recent simulations showing a distinct order parameter exponent (β).
Conclusions:
- The study clarifies the universality class and crossover behavior of random resistor-diode networks.
- Theoretical predictions are consistent with experimental simulations.
- Further refinement of the theory for isotropic-directed percolation crossover is provided.
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