Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1998-06-18
Physics
Condensed Matter
Disordered Systems and Neural Networks
14 pages, 7 figures, LaTeX, submitted to J. Phys. A: Math. Gen, added references, corrected typos
Scientific paper
10.1088/0305-4470/31/40/009
Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices. Systems L x L x L' with L' >> L were studied for both bond (s.c., f.c.c., b.c.c.) and site (f.c.c.) percolation. The excess number of clusters $\tilde {b}$ per unit length was confirmed to be a universal quantity with a value $\tilde {b} \approx 0.412$. Likewise, the critical crossing probability in the L' direction, with periodic boundary conditions in the L x L plane, was found to follow a universal exponential decay as a function of r = L'/L for large r. Simulations were also carried out to find new precise values of the critical thresholds for site percolation on the f.c.c. and b.c.c. lattices, yielding $p_c(f.c.c.)= 0.199 236 5 \pm 0.000 001 0$, $p_c(b.c.c.)= 0.245 961 5\pm 0.000 001 0$.
Lorenz Christian D.
Ziff Robert M.
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