### 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 d_{f}=1.86±0.02 and d_{BB}=1.80±0.03, respectively.

Original language | English (US) |
---|---|

Pages (from-to) | 3682-3693 |

Number of pages | 12 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 4 SUPPL. B |

State | Published - Apr 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*53*(4 SUPPL. B), 3682-3693.

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 4 SUPPL. B, pp. 3682-3693.

}

TY - JOUR

T1 - Generic rigidity percolation in two dimensions

AU - Jacobs, D. J.

AU - Thorpe, Michael

PY - 1996/4

Y1 - 1996/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000785337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000785337&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000785337

VL - 53

SP - 3682

EP - 3693

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4 SUPPL. B

ER -