Christian D Lorenz and Robert M Ziff 1998 J. Phys. A: Math. Gen. 31 8147 doi:10.1088/0305-4470/31/40/009
Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
Christian D Lorenz and Robert M Ziff
Show affiliationsExtensive 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.
- PACS
-
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
-
11K45 Pseudo-random numbers; Monte Carlo methods
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
-
Issue 40 (9 October 1998)
Received 1 July 1998
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Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
Christian D Lorenz and Robert M Ziff 1998 J. Phys. A: Math. Gen. 31 8147
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