A method based on the symmetry of bonding directions i = 1, 2, …, n is introduced to estimate the critical probability pc in bond percolation problems. The leading terms in the critical equation Q(p1, p2,…, pi,…, pn) = 1 are derived for some two‐ and three‐dimensional lattices and consequently pc can be evaluated by setting all pi's equal. In two dimensions the three exact, known values of pc are regained in addition to an estimate for the kagome lattice pc≃0.535. In three dimensions a one‐parameter fitting to diamond and bcc lattices gives for simple cubic lattice the estimate pc ≃ 0.258 in agreement with its lower limit 1/4.

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© 1974 American Institute of Physics.
1974
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