A scaling theory to derive the dependence of the average number <k> of spanning clusters at the high-dimensional percolation threshold was presented. It was found that the average number <k> should become independent of L for dimensions d<6 and vary as ln L at d=6. It was also found that the predictions for d>6 depend on the boundary conditions. The results show that simulation in six dimensions are consistent with this prediction whereas in five dimensions the average number of spanning clusters still increases as ln L even up to L=201.
|Number of pages||7|
|Journal||Physical Review E|
|State||Published - 1 Nov 2004|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics