Critical exponents for the conductivity of random resistor lattices

1977/06/15 by Joseph P. Straley · 2 citations
Computer Science · Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Theoretical and Computational Physics #Topological and Geometric Data Analysis

paper · doi:10.1103/physrevb.15.5733

openalex publication_date 1977/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

This paper presents three results concerning the critical exponents which characterize the conduction threshold of a resistor lattice. (a) There are no rigorous inequalities similar to those for the phase-transition critical exponents. (b) There is a dual transformation in two dimensions which relates the critical exponents: in particular s=t, u=(1)/(2) for the two-dimensional bond problem. (c) The exponents for the two- and three-dimensional bond and site problems are estimated by numerically solving for the voltage distributions of large finite disordered lattices. The results are in agreement with the "scaling" exponent relationship.

Citations

• The theory of equilibrium critical phenomena
• An introduction to percolation theory

Cited by

• Conductivity exponents at the percolation threshold
• A coarse-graining theory for elliptic operators and homogenization in high contrast

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