Department of Physics Papers

Document Type

Journal Article

Date of this Version

10-18-2005

Publication Source

Physical Review E

Volume

72

Start Page

046123-1

Last Page

046123-17

DOI

10.1103/PhysRevE.72.046123

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.

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Date Posted: 20 August 2015

This document has been peer reviewed.