The cavity method for the rigidity transition

J. Barré; A. R. Bishop; T. Lookman; A. Saxena

doi:10.1007/s10955-004-2709-2

The cavity method for the rigidity transition

J. Barré
, A. R. Bishop
, T. Lookman
, A. Saxena

Los Alamos National Laboratory Theoretical Division

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level.

Original language	English
Pages (from-to)	1057-1071
Number of pages	15
Journal	Journal of Statistical Physics
Volume	118
Issue number	5-6
DOIs	https://doi.org/10.1007/s10955-004-2709-2
State	Published - Mar 2005
Externally published	Yes

Keywords

Cavity method
Combinatorial optimization
Rigidity transition

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10.1007/s10955-004-2709-2

Cite this

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abstract = "In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level.",

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AU - Barré, J.

AU - Bishop, A. R.

AU - Lookman, T.

AU - Saxena, A.

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N2 - In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level.

AB - In order to motivate an analogy between the rigidity theory and combinatorial optimization, we have used the cavity method to study the floppy to rigid transition in a 2-dimensional (2D) random graph as well as in a 3D small world chain. Our analytic results are in excellent agreement with numerical studies using the pebble game algorithm. We also illustrate that a transfer matrix method is equivalent to the cavity method at the replica symmetric level.

KW - Cavity method

KW - Combinatorial optimization

KW - Rigidity transition

UR - https://www.scopus.com/pages/publications/17544370119

U2 - 10.1007/s10955-004-2709-2

DO - 10.1007/s10955-004-2709-2

M3 - 文章

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VL - 118

SP - 1057

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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ER -

The cavity method for the rigidity transition

Abstract

Keywords

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