Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
Lorenz, Christian D.; Ziff, Robert M.
1998-10-09
Citation
Lorenz, Christian D; Ziff, Robert M (1998). "Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation ." Journal of Physics A: Mathematical and General. 31(40): 8147-8157. <http://hdl.handle.net/2027.42/48837>
Abstract
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 with were studied for both bond (s.c., f.c.c., b.c.c.) and site (f.c.c.) percolation. The excess number of clusters per unit length was confirmed to be a universal quantity with a value . Likewise, the critical crossing probability in the direction, with periodic boundary conditions in the plane, was found to follow a universal exponential decay as a function of 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 , . We also report the value for site percolation.Publisher
IOP Publishing Ltd
ISSN
0305-4470
Types
Article
Metadata
Show full item recordAccessibility: If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.