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Universality of 3D percolation exponents and first-order corrections to scaling for conductivity exponents

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  • Kozlov, B.
  • Laguës, M.

Abstract

By using a fast, Nested Dissection algorithm we compare the results of finite-size scaling at pc and of “p” scaling (L=const) on large cubic random resistor networks [up to 500×500×500]. The “p” scaling for conductivity of both site and bond networks leads to an exponent t=2.00(1). The finite-size scaling leads to the ratio of this conductivity exponent to the coherence length exponent ν: t/ν=2.283(3). Combining these results we estimate ν=0.876(6), in excellent agreement with a value proposed by Ballesteros et al. The first-order correctional exponent ω is found to be ω=1.0(2).

Suggested Citation

  • Kozlov, B. & Laguës, M., 2010. "Universality of 3D percolation exponents and first-order corrections to scaling for conductivity exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5339-5346.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:23:p:5339-5346
    DOI: 10.1016/j.physa.2010.08.002
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    References listed on IDEAS

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    1. J.P. Clerc & V.A. Podolskiy & A.K. Sarychev, 2000. "Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 15(3), pages 507-516, June.
    2. Chunyu Li & Tsu-Wei Chou, 2009. "Precise Determination Of Backbone Structure And Conductivity Of 3d Percolation Networks By The Direct Electrifying Algorithm," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 423-433.
    3. Jean-Marie Normand & Hans J. Herrmann, 1995. "Precise Determination Of The Conductivity Exponent Of 3d Percolation Using "Percola"," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(06), pages 813-817.
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    Cited by:

    1. Balankin, Alexander S., 2024. "A survey of fractal features of Bernoulli percolation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Lambrou, Eleftherios & Gergidis, Leonidas N., 2024. "A computational method for calculating the electrical and thermal conductivity of random composites," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 642(C).

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