Exact relations between critical exponents for elastic stiffness and electrical conductivity of two-dimensional percolating networks

David J. Bergman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

It has long been known that the critical exponent T of the elastic stiffness [formula presented] of a d-dimensional percolating network [formula presented] measures the closeness of the network to its percolation threshold [formula presented] satisfies the following inequalities: [formula presented] where t is the critical exponent of the electrical conductivity [formula presented] of the same network and [formula presented] is the critical exponent of the percolation correlation length [formula presented] Similarly, the critical exponents that characterize the divergences [formula presented] [formula presented] of a rigid or normal and a superconducting or normal random mixture [formula presented] now measures the closeness of the rigid or superconducting constituent to its percolation threshold [formula presented] have long been known to satisfy [formula presented] We now show that, when [formula presented] T is in fact exactly equal to [formula presented] and S is exactly equal to s.

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