• DOI:10.1088/0305-4470/31/40/009
• Corpus ID: 12493873

Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation

@article{Lorenz1998UniversalityOT,
  title={Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation},
  author={Christian D. Lorenz and Robert M. Ziff},
  journal={Journal of Physics A},
  year={1998},
  volume={31},
  pages={8147-8157}
}

• C. Lorenz, R. Ziff
• Published 18 June 1998
• Physics
• Journal of Physics A

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-centred cubic (f.c.c.), and body-centred cubic (b.c.c.) lattices. Systems L L L0 with L0 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 Q b per unit length was confirmed to be a universal quantity with a value Q b 0:412. Likewise, the critical crossing probability in the L0 direction, with periodic boundary conditions in theLL plane, was found to follow a universal exponential decay as a function of r D L 0 =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 pc.f:c:c:/D 0:199 2365 0:000 0010, pc.b:c:c:/D 0:245 9615 0:000 0010. We also report the value pc.s:c:/D 0:311 6080 0:000 0004 for site percolation.