Scaling of splay and total rigidity for elastic percolation on the triangular lattice

The randomly diluted elastic network with central force interactions is simulated on the triangular lattice using a constraint analysis of cluster displacement vectors. The exponents for the percolation of splay and total rigidity are found to be the same, {ν}=1.14±{}0.1, {γ}=1.6±{}0.3, and {β}=0.46±{}0.4. The concentration of bonds that are in clusters rigid only with respect to a splay deformation is evaluated as a function of bond concentration. The area under the resulting distribution diminishes with lattice size as {~}L^-1.1, indicating that splay and total rigidity have the same threshold, pc{}0.64.