Number of spanning clusters at the high-dimensional percolation thresholds

Details Number of spanning clusters at the high-dimensional percolation thresholds Number of spanning clusters at the high-dimensional percolation thresholds

2004-07-11

arxiv.org/abs/cond-mat/0407276v2

Physics

Condensed Matter

Statistical Mechanics

8 pages, 11 figures. Final version to appear on Physical Review E

Scientific paper

10.1103/PhysRevE.70.056116

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.

Affiliated with

Also associated with

No associations

Rating

Number of spanning clusters at the high-dimensional percolation thresholds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Number of spanning clusters at the high-dimensional percolation thresholds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Number of spanning clusters at the high-dimensional percolation thresholds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-158224