PERCOLATION THRESHOLDS, CRITICAL EXPONENTS, AND SCALING FUNCTIONS ON SPHERICAL RANDOM LATTICES AND THEIR DUALS

Ming-Chang Huang () and Hsiao-Ping Hsu ()
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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;

International Journal of Modern Physics C (IJMPC), 2002, vol. 13, issue 03, 383-395

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.

Keywords: Percolation threshold; critical exponent; scaling function; spherical random lattice (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S012918310200319X

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