Abstract
Arguments are presented to demonstrate that exact equality relations exist between the critical exponents which characterize the macroscopic conductivity σ e and the macroscopic elastic stiffness moduli C e of percolating systems of any dimensionality. Using the notation σ e ∝Δp t, C e ∝Δp T for the critical behavior of a randomly diluted system slightly above the percolation threshold p c , (Δp≡p−p c >0) and σ e ∝|Δp|−s, C e ∝|Δp|−S for the critical behavior of a random mixture of normal and perfectly conducting or normal and perfectly rigid constituents slightly below that threshold, (Δp≡p−p c <0) we show that T=t+2ν and S=s, where ν is the percolation correlation length critical exponent ξ∝|Δp|−ν (Δp≷0).
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Bergman, D.J. Exact Relations Between Elastic and Electrical Response of d-Dimensional Percolating Networks with Angle-Bending Forces. Journal of Statistical Physics 111, 171–199 (2003). https://doi.org/10.1023/A:1022205007823
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DOI: https://doi.org/10.1023/A:1022205007823