%0 Journal Article %1 Ellenbroek2011Rigidity %A Ellenbroek, Wouter G. %A Mao, Xiaoming %D 2011 %J EPL (Europhysics Letters) %K rigidity percolation lattice-models %P 54002+ %R 10.1209/0295-5075/96/54002 %T Rigidity percolation on the square lattice %U http://dx.doi.org/10.1209/0295-5075/96/54002 %X The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest-neighbor bonds. This constitutes a rigidity percolation transition which we study analytically by mapping it to a connectivity problem of two-colored random graphs. We derive an exact recurrence equation for the probability of having a rigid percolating cluster and solve it in the infinite volume limit. From this solution we obtain the rigidity threshold as a function of system size, and find that, in the thermodynamic limit, there is a mixed first-order–second-order rigidity percolation transition at the isostatic point.

@article{Ellenbroek2011Rigidity, abstract = {{The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest-neighbor bonds. This constitutes a rigidity percolation transition which we study analytically by mapping it to a connectivity problem of two-colored random graphs. We derive an exact recurrence equation for the probability of having a rigid percolating cluster and solve it in the infinite volume limit. From this solution we obtain the rigidity threshold as a function of system size, and find that, in the thermodynamic limit, there is a mixed first-order–second-order rigidity percolation transition at the isostatic point.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Ellenbroek, Wouter G. and Mao, Xiaoming}, biburl = {https://www.bibsonomy.org/bibtex/2fe10a01b4a3f5e00d03797d6a922f593/nonancourt}, citeulike-article-id = {10374409}, citeulike-linkout-0 = {http://dx.doi.org/10.1209/0295-5075/96/54002}, day = 01, doi = {10.1209/0295-5075/96/54002}, interhash = {df3d70c3dcfceb0c8c5602953306c4fd}, intrahash = {fe10a01b4a3f5e00d03797d6a922f593}, journal = {EPL (Europhysics Letters)}, keywords = {rigidity percolation lattice-models}, month = dec, pages = {54002+}, posted-at = {2012-02-21 17:45:21}, priority = {2}, timestamp = {2019-08-01T15:36:09.000+0200}, title = {{Rigidity percolation on the square lattice}}, url = {http://dx.doi.org/10.1209/0295-5075/96/54002}, year = 2011 }