Journal
EPL
Volume 96, Issue 5, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1209/0295-5075/96/54002
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Funding
- U.S. National Science Foundation [DMR-0804900]
- U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering [DE-FG02-05ER46199]
- Netherlands Organisation for Scientific Research (NWO)
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [0804900] Funding Source: National Science Foundation
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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. Copyright (C) EPLA, 2011
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