Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices

Details Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices

1997-10-03

arxiv.org/abs/cond-mat/9710044v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pgs, 7 figures, LaTeX, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.57.230

Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide very precise values of the critical thresholds for each of the lattices: pc(s.c.) = 0.248 812 6(5), pc(f.c.c.) = 0.120 163 5(10), and pc(b.c.c.) = 0.180 287 5(10). For p close to pc, the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent $tau$ (2.189(2)), the finite-size correction exponent $omega$ (0.64(2)), and the scaling function exponent $sigma$ (0.445(1)) confirmed to be universal.

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