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Site-bond percolation problems

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Abstract

We study a percolation process in which both sites and bonds are randomly blocked, independent of each other. In the Bethe lattice, the exact solution for the percolation threshold is found to be a hyperbola in thex-p plane, wherex andp are the respective probabilities of each site and bond being unblocked. Percolation threshold for a square and a simple cubic lattice is obtained by computer simulation. We also present a result obtained by a real-space renormalization group technique for the square lattice.

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Authors and Affiliations

  1. Department of Physics, Brandeis University, 02254, Waltham, Massachusetts

    K. C. Chang & T. Odagaki

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  1. K. C. Chang
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  2. T. Odagaki
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Chang, K.C., Odagaki, T. Site-bond percolation problems. J Stat Phys 35, 507–516 (1984). https://doi.org/10.1007/BF01010823

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  • DOI: https://doi.org/10.1007/BF01010823

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