1/d expansion for k -core percolation

A. B. Harris, J. M. Schwarz

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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
Issue number4
StatePublished - Oct 2005
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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