Percolation in hyperbolic lattices

Kim, Beom Jun (author): Department of Physics, BK21 Physics Research Division, Sungkyunkwan University, Suwon 440-746, Korea

(creator_code:org_t)

American Physical Society, 2009
2009
English.
In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1063-651X .- 1095-3787. ; 79:1, s. 011124-011130

Related links:: http://link.aps.org/...; show more...; https://urn.kb.se/re...; https://doi.org/10.1...; show less...

Abstract Subject headings

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.

About the subject

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