Hierarchical models of rigidity percolation
Statistical Mechanics
2015-05-13 v2
Abstract
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.
Cite
@article{arxiv.0907.4233,
title = {Hierarchical models of rigidity percolation},
author = {J. Barré},
journal= {arXiv preprint arXiv:0907.4233},
year = {2015}
}
Comments
20 pages, 8 figures. Figures improved, references added, small modifications. Accepted in Phys. Rev. E