Percolation on hyperbolic lattices

Details Percolation on hyperbolic lattices Percolation on hyperbolic lattices

2009-01-05

arxiv.org/abs/0901.0483v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 18 figures, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.79.011124

The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.

Affiliated with

Also associated with

No associations

Rating

Percolation on hyperbolic lattices 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 Percolation on hyperbolic lattices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Percolation on hyperbolic lattices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-35010