EXACT RELATIONS BETWEEN CRITICAL EXPONENTS FOR ELASTIC STIFFNESS AND ELECTRICAL CONDUCTIVITY OF PERCOLATING NETWORKS

摘要

The exponents which describe the critical behavior of the macroscopic elastic stiffness moduli (T, S) and the macroscopic electrical conductivity (t, s) of a two-constituent composite near a percolation threshold have recently been shown to obey the following exact relationships: T = t + 2v, S = s, where v is the percolation correlation length critical exponent [see D.J. Bergman, J. Stat. Phys. 111, 171-199 (2003)]. The proofs of these exact relationships are based on some assumptions that need to be verified. The essential elements of those proofs are reviewed, and the assumptions on which they depend are described and discussed, including techniques by which they could be tested.