Explosive percolation on the Bethe lattice is ordinary

Young Sul Cho ()
Additional contact information
Young Sul Cho: Jeonbuk National University

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 5, 1-6

Abstract: Abstract The Achlioptas process, which suppresses the aggregation of large-sized clusters, can exhibit an explosive percolation (EP) where the order parameter emerges abruptly yet continuously in the thermodynamic limit. It is known that EP is accompanied by an abnormally small critical exponent of the order parameter. In this paper, we report that a novel type of EP occurs on a Bethe lattice, where the critical exponent of the order parameter is the same as in ordinary bond percolation based on numerical analysis. This is likely due to the property of a finite Bethe lattice that the number of sites on the surface with only one neighbor is extensive to the system size. To overcome this finite size effect, we consider an approximate size of the cluster that each site on the surface along its branch belongs to, and accordingly approximate the sizes of an extensive number of clusters during simulation. As a result, the Achlioptas process becomes ineffective and the order parameter behaves like that of ordinary percolation at the threshold. We support this result by measuring other critical exponents as well. Graphicabstract

Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-024-00699-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:97:y:2024:i:5:d:10.1140_epjb_s10051-024-00699-z

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-024-00699-z

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().