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Conductivity exponent and backbone dimension in 2-d percolation

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  • Grassberger, Peter

Abstract

We present high statistics simulations for 2-d percolation clusters in the “bus bar” geometry at the critical point, for site and for bond percolation. We measured their backbone sizes and electrical conductivities. For all sets of measurements we find large corrections to scaling, most of which do not seem to be described by single powers. Using single power terms for the corrections to scaling of the backbone masses, we would obtain fractal dimensions which are different for site and bond percolation, while the correct result is Db=1.6432±0.0008 for both. For the conductivity, the corrections to scaling are strongly non-monotonic for bond percolation. The exponent t′=t/ν is measured as 0.9826±0.0008, in disagreement with the Alexander–Orbach and other conjectures.

Suggested Citation

  • Grassberger, Peter, 1999. "Conductivity exponent and backbone dimension in 2-d percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 262(3), pages 251-263.
    • Handle: RePEc:eee:phsmap:v:262:y:1999:i:3:p:251-263
    DOI: 10.1016/S0378-4371(98)00435-X
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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. Zhang, Zhongjin & Hou, Pengcheng & Fang, Sheng & Hu, Hao & Deng, Youjin, 2021. "Critical exponents and universal excess cluster number of percolation in four and five dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    3. Stanley, H.Eugene & Andrade, José S. & Havlin, Shlomo & Makse, Hernán A. & Suki, Béla, 1999. "Percolation phenomena: a broad-brush introduction with some recent applications to porous media, liquid water, and city growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 5-16.
    4. Stanley, H.Eugene & Andrade, José S, 2001. "Physics of the cigarette filter: fluid flow through structures with randomly-placed obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 17-30.
    5. Gross, Bnaya & Bonamassa, Ivan & Havlin, Shlomo, 2021. "Interdependent transport via percolation backbones in spatial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).

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