1/d expansion for k -core percolation

A. B. Harris, Jennifer M Schwarz

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The physics of k -core percolation pertains to those systems whose constituents require a minimum number of k connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from orientational ordering in solid ortho-para H2 mixtures to the onset of rigidity in bar-joint networks to dynamical arrest in glass-forming liquids. Unlike ordinary (k=1) and biconnected (k=2) percolation, the mean field k≥3 -core percolation transition is both continuous and discontinuous, i.e., there is a jump in the order parameter accompanied with a diverging length scale. To determine whether or not this hybrid transition survives in finite dimensions, we present a 1/d expansion for k -core percolation on the d -dimensional hypercubic lattice. We show that to order 1/d3 the singularity in the order parameter and in the susceptibility occur at the same value of the occupation probability. This result suggests that the unusual hybrid nature of the mean field k -core transition survives in high dimensions.

Original languageEnglish (US)
Article number046123
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume72
Issue number4
DOIs
StatePublished - Oct 2005
Externally publishedYes

Fingerprint

expansion
Order Parameter
Mean Field
rigidity
Length Scale
Susceptibility
occupation
Rigidity
Higher Dimensions
Jump
Physics
Clustering
Singularity
Liquid
magnetic permeability
physics
glass
liquids
Range of data
Glass

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

1/d expansion for k -core percolation. / Harris, A. B.; Schwarz, Jennifer M.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 4, 046123, 10.2005.

Research output: Contribution to journalArticle

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