Conductivity exponents at the percolation threshold
Clinton DeW. Van Siclen
TL;DR
This paper explores the relationships between different percolation problems, deriving formulas for conductivity exponents across dimensions and calculating their values in 2D and 3D systems.
Contribution
It establishes new relations between critical exponents in two-component and conductor/insulator percolation problems, providing formulas connecting conductivity exponents in various dimensions.
Findings
Derived relations between critical exponents in different percolation problems.
Calculated conductivity exponents for 2D and 3D systems.
Suggested formulas linking exponents across dimensions.
Abstract
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different dimensions. Values for the critical exponents are obtained from calculations on the incipient infinite cluster in two and three dimensions.
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Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Surface and Thin Film Phenomena