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Divergence of the bulk resistance at criticality in disordered media

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Consider the electrical resistancer n (p) of a hypercubic bond lattice [O,n]d inZ d, where the bonds have resistance 1Ω with probabilityp or ∞ with probability 1-p. Letp n (p)=n 2-d r n (p) andp(p)=limn→∞pn(p). It is well known thatp(p)<∞ ifp>p c andp(p)=∞ ifp<p c , wherep c is the percolation threshold. Here we show thatp(p c )=∞, and\(\lim _{p \downarrow p_c } \rho (p) = \rho (p_c ) = \infty \).

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Communicated by J. L. Lebowitz

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Zhang, Y. Divergence of the bulk resistance at criticality in disordered media. J Stat Phys 84, 263–267 (1996). https://doi.org/10.1007/BF02179585

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Key Words

  • Bulk resistance
  • criticality