Critical exponents for the conductivity of random resistor lattices 论文
1977Physical review. B, Solid state引用 444
Theoretical and Computational PhysicsMaterial Dynamics and PropertiesTopological and Geometric Data Analysis
详细信息
- 发表期刊/会议
- Physical review. B, Solid state
- 发表日期
- 1977-06-15
- 发表年份
- 1977
关键词
Theoretical and Computational PhysicsMaterial Dynamics and PropertiesTopological and Geometric Data Analysis
摘要
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.