Generic rigidity percolation in two dimensions

D. J. Jacobs, Michael Thorpe

Research output: Contribution to journalArticle

145 Citations (Scopus)

Abstract

We study rigidity percolation for random central-force networks on the bond- and site-diluted generic triangular lattice. Here, each site location is randomly displaced from the perfect lattice, removing any special symmetries. Using the pebble game algorithm, the total number of floppy modes are counted exactly, and exhibit a cusp singularity in the second derivative at the transition from a rigid to a floppy structure. The critical thresholds for bond and site dilution are found to be 0.66020±0.0003 and 0.69755±0.0003, respectively. The network is decomposed into unique rigid clusters, and we apply the usual percolation scaling theory. From finite size scaling, we find that the generic rigidity percolation transition is second order, but in a different universality class from connectivity percolation, with the exponents α= -0.48±0.05, α=0.175±0.02, and ν= 1.21±0.06. The fractal dimension of the spanning rigid clusters and the spanning stressed regions at the critical threshold are found to be df=1.86±0.02 and dBB=1.80±0.03, respectively.

Original languageEnglish (US)
Pages (from-to)3682-3693
Number of pages12
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number4 SUPPL. B
StatePublished - Apr 1996
Externally publishedYes

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rigidity
Rigidity
Critical Threshold
Two Dimensions
Percolation Theory
Scaling Theory
Triangular Lattice
Finite-size Scaling
Cusp
Second derivative
scaling
Fractal Dimension
Universality
thresholds
games
Connectivity
cusps
Exponent
Singularity
Game

ASJC Scopus subject areas

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

Cite this

Generic rigidity percolation in two dimensions. / Jacobs, D. J.; Thorpe, Michael.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 53, No. 4 SUPPL. B, 04.1996, p. 3682-3693.

Research output: Contribution to journalArticle

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