Rigidity percolation on the square lattice

Details Rigidity percolation on the square lattice Rigidity percolation on the square lattice

2011-07-20

arxiv.org/abs/1107.3933v1

Europhysics Letters 96, 54002 (2011)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 3 figures

Scientific paper

10.1209/0295-5075/96/54002

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.

Affiliated with

Also associated with

No associations

Rating

Rigidity percolation on the square lattice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rigidity percolation on the square lattice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigidity percolation on the square lattice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-34707