Topology of a two-component disordered system below and above the percolation threshold
- 1 March 1982
- journal article
- research article
- Published by Taylor & Francis in Philosophical Magazine Part B
- Vol. 45 (3) , 335-346
- https://doi.org/10.1080/13642818208246409
Abstract
The influence of geometry of a two-component system composed of randomly distributed metal and dielectric regions on various kinetic coefficients (conductivity, Hall effect in a weak magnetic field, thermoelectric power) is studied near the percolation threshold. Rigorous mathematical theorems for the conductivity and Hall effect in the critical regimes are stated. A new correlation length, called here the infinite-cluster macrobond length, is defined and its critical exponent calculated to be ã(p) α δp −g at p → pc + 0, where g = 1.4 ± 0.1 in 2-D space and g = 0.98 ± 0.1 in 3-D space.Keywords
This publication has 12 references indexed in Scilit:
- Percolation theory and transport coefficients in disordered systemsPhilosophical Magazine Part B, 1982
- On a relation between percolation theory and the elasticity of gelsJournal de Physique Lettres, 1976
- The nature of percolation ‘channels’Solid State Communications, 1973
- Hall Effect of an Inhomogeneous MaterialJournal of Applied Physics, 1972
- Percolation Theory and Electrical ConductivityPhysical Review Letters, 1971
- The scaling laws for percolation processesJournal of Physics C: Solid State Physics, 1971
- An introduction to percolation theoryAdvances in Physics, 1971
- Monte Carlo Solution of Bond Percolation Processes in Various Crystal LatticesBell System Technical Journal, 1962
- Cluster Size in Random Mixtures and Percolation ProcessesPhysical Review B, 1961
- Equivalence of the Critical Concentrations in the Ising and Heisenberg Models of FerromagnetismPhysical Review Letters, 1960