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    Conductance Distributions in Random Resistor Networks: Self Averaging and Disorder Lengths

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    The self averaging properties of conductance gg are explored in random resistor networks with a broad distribution of bond strengths P(g)\simg^{\mu-1}. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of size LL and distribution tail parameter μ\mu. For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit μ\mu --> 0. A {\it disorder length} ξD\xi_D is identified beyond which the system is effectively homogeneous. This length diverges as ξDμν\xi_D \sim |\mu|^{-\nu} (ν\nu is the regular percolation correlation length exponent) as μ\mu-->0. This suggest that exactly the same critical behavior can be induced by geometrical disorder and bu strong bond disorder with the bond occupation probability ppμ\mu. Only lattices at the percolation threshold have renormalized probability distribution in a {\it Levy-like} basin. At the threshold the disorder length diverges at a vritical tail strength μc\mu_c as μμcz|\mu-\mu_c|^{-z}, with z=3.2±0.1z=3.2\pm 0.1, a new exponent. Critical path analysis is used in a generalized form to give form to give the macroscopic conductance for lattice above pcp_c.Comment: 16 pages plain TeX file, 6 figures available upon request.IBC-1603-01
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