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Critical exponents for the conductivity of random resistor lattices
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 $s=t$, $u=\frac{1}{2}$ 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.
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Citations
Cites
Kirkpatrick, S. (1973) · Reviews of Modern Physics · doi:10.1103/revmodphys.45.574 · Cited by 5,260
Cited by
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Physics of inhomogeneous inorganic materials
Nan, C.-W. (1993) · Progress in Materials Science · doi:10.1016/0079-6425(93)90004-5 · Cited by 1,050
Bergman, D. J., & Imry, Y. (1977) · Physical Review Letters · doi:10.1103/physrevlett.39.1222 · Cited by 447
Dielectric spectroscopy on melt processed polycarbonate—multiwalled carbon nanotube composites
Pötschke, P., Dudkin, S. M., & Alig, I. (2003) · Polymer · doi:10.1016/s0032-3861(03)00451-8 · Cited by 447
Tanner, D. B. (2019) · doi:10.1017/9781316672778 · Cited by 106
Metadata
- Authors
- Straley, J. P.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1977-06-15
- Volume
- 15
- Issue
- 12
- Pages
- 5733-5737
- ISSN
- 0556-2805 (ISSN-L)
- OpenAlex
- W2035473948
- Cited by
- 445
- References
- 1
- FWCI
- 7.68
- Type
- journal article
- Language
- en
- Open access
- closed
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