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Multifractal properties of the random resistor network
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Summary
This study reveals that in 2D random resistor networks at percolation, small currents follow a P(i) ~ 1/i distribution. This implies moments of current do not exist, with low currents sharing the backbone
Area of Science:
- Condensed matter physics
- Statistical physics
- Network science
Background:
- Percolation theory describes the behavior of connected systems near a critical threshold.
- Random resistor networks are fundamental models in statistical physics.
Purpose of the Study:
- Investigate the multifractal spectrum of electrical current in 2D random resistor networks at the percolation threshold.
- Analyze current distribution under different voltage application methods (parallel bars vs. points).
Main Methods:
- Numerical simulations of two-dimensional random resistor networks.
- Analysis of current probability distributions and their moments.
- Characterization of fractal dimensions of network components.
Main Results:
- The probability distribution of small currents follows P(i) ~ 1/i in the infinite system limit.
- Moments of the current of order q <= 0 do not exist.
- Low currents exhibit the fractal dimension of the network backbone.
Conclusions:
- The current distribution in these networks is highly heterogeneous.
- The network backbone can be characterized by fractal blobs and high-current carrying bonds.
- Understanding current flow is crucial for disordered systems at criticality.
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