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Percolation Thresholds, Critical Exponents, And Scaling Functions On Spherical Random Lattices And Their Duals

Author

Listed:
  • MING-CHANG HUANG

    (Department of Physics, Chung-Yuan Christian University, Chungli, 320, Taiwan, ROC)

  • HSIAO-PING HSU

    (Department of Physics, Chung-Yuan Christian University, Chungli, 320, Taiwan, ROC;
    Computing Centre, Academia Sinica, Taipei, 11529, Taiwan, ROC;
    John-von-Neumann Institute for Computing, Forschungszentrum Jülich, Jülich, D-52425, Germany)

Abstract

Bond-percolation processes are studied for random lattices on the surface of a sphere, and for their duals. The estimated threshold is 0.3326 ± 0.0005 for spherical random lattices and 0.6680 ± 0.0005 for the duals of spherical random lattices, and the exact threshold is conjectured as 1/3 for two-dimensional random lattices and 2/3 for their duals. A suitably defined spanning probability at the threshold,Ep(pc), for both spherical random lattices and their duals is 0.980±0.005, which may be universal for a 2-d lattice with this spanning definition. The shift-to-width ratio of the distribution function of the threshold concentration and the universal values of the critical value of the effective coordination number can be extended from regular lattices to spherical random lattices and their duals. The results of critical exponents are consistent with the assertion from the universality hypothesis. Finite-size scaling is also examined.

Suggested Citation

  • Ming-Chang Huang & Hsiao-Ping Hsu, 2002. "Percolation Thresholds, Critical Exponents, And Scaling Functions On Spherical Random Lattices And Their Duals," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 383-395.
    • Handle: RePEc:wsi:ijmpcx:v:13:y:2002:i:03:n:s012918310200319x
    DOI: 10.1142/S012918310200319X
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