Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe lattices

P. M. Duxbury, D. J. Jacobs, M. F. Thorpe, C. Moukarzel

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


We show that the negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heatcan be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.

Original languageEnglish (US)
Pages (from-to)2084-2092
Number of pages9
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number2
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

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


Dive into the research topics of 'Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe lattices'. Together they form a unique fingerprint.

Cite this