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The Cavity Method for the Rigidity Transition

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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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Authors and Affiliations

  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

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

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  1. J. Barré
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  2. A. R. Bishop
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  3. T. Lookman
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  4. A. Saxena
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Correspondence to J. Barré.

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Barré, J., Bishop, A.R., Lookman, T. et al. The Cavity Method for the Rigidity Transition. J Stat Phys 118, 1057–1071 (2005). https://doi.org/10.1007/s10955-004-2709-2

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  • DOI: https://doi.org/10.1007/s10955-004-2709-2

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