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 ∼$L^{\mathrm{-}1.1}$, indicating that splay and total rigidity have the same threshold, $p_c$≊0.64.