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 , 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.
- Received 3 May 1976
DOI:https://doi.org/10.1103/PhysRevB.15.5733
©1977 American Physical Society