Surface and bulk criticality in midpoint percolation
2010 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 81, no 4, 1108-6 sidor p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 81, no 4, 1108-6 sidor p.
percolation, surface criticality
Condensed Matter Physics
Research subject Theoretical Physics
IdentifiersURN: urn:nbn:se:umu:diva-35224DOI: 10.1103/PhysRevE.81.041108ISI: 000277265700016OAI: oai:DiVA.org:umu-35224DiVA: diva2:338023