Rigidity percolation on the square lattice

W.G. Ellenbroek, Xiaoming Mao

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)


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.
Original languageEnglish
Article number54002
Pages (from-to)54002-1/6
Issue number12
Publication statusPublished - 2011


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