AI Article Synopsis
- Percolation clusters are random fractals examined through probability distribution functions to understand their geometrical and transport properties.
- Using renormalized field theory, researchers analyze the behavior of these distribution functions in varying scaling limits.
- The study focuses on several aspects, such as pair-connection probability and self-avoiding walks, deriving results valid for any complexity of the perturbation theory.
Article Abstract
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds, and the shortest, the longest, and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.
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| http://dx.doi.org/10.1103/PhysRevE.79.011128 | DOI Listing |
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