Surface and bulk criticality in midpoint percolation

The concept of midpoint percolation has recently been applied tocharacterize the double percolation transitions in negatively curvedstructures. Regular $d$-dimensional hypercubic lattices are in the presentwork investigated using the same concept.Specifically, the site-percolation transitions at the critical thresholds areinvestigated for dimensions up to $d=10$ by means of the Leath algorithm.It is shown that the explicit inclusion of the boundariesprovides a straightforward way to obtain critical indices, both for thebulk and surface parts. At and above the critical dimension $d=6$, it isfound that the percolation cluster contains only a finite number of surfacepoints in the infinite-size limit. This is in accordance with theexpectation from studies of lattices with negative curvature. It is alsofound that the number of surface points, reached by the percolation clusterin the infinite limit, approaches $2d$ for large dimensions $d$. We alsonote that the size dependence in proliferation of percolatingclusters for $d\ge 7$ can be obtained by solely counting surface pointsof the midpoint cluster.

Minnhagen, PetterUmeå universitet,Institutionen för fysik(Swepub:umu)pemi0001 (author)
Kim, Beom JunDept. of Physics, Sungkyunkwan University, Suwon, Korea (author)
Umeå universitetInstitutionen för fysik (creator_code:org_t)

In:Physical Review E. Statistical, Nonlinear, and Soft Matter Physics81:4, s. 1108-6 sidor1063-651X1095-3787

By the author/editor: Baek, Seung Ki, ...; Minnhagen, Pette ...; Kim, Beom Jun

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Physical Science ...; and Condensed Matter ...

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