Hierarchical models of rigidity percolation

Details Hierarchical models of rigidity percolation Hierarchical models of rigidity percolation

2009-07-24

arxiv.org/abs/0907.4233v2

Physics

Condensed Matter

Statistical Mechanics

20 pages, 8 figures. Figures improved, references added, small modifications. Accepted in Phys. Rev. E

Scientific paper

We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order to avoid stressed bonds may change the phase diagram. In contrast to what happens on random graphs and in some recent numerical studies at zero temperature, we do not find a true intermediate phase separating the usual rigid and floppy ones.

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