Stressed Backbone and Elasticity of Random Central-Force Systems

We use a new algorithm to find the stress-carrying backbone of "generic" site-diluted triangular lattices of up to ${10}^6$ sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold is $p_c=0.6975\mathrm{}\pm 0.0003$, the correlation length exponent $\nu =1.16\mathrm{}\pm 0.03$, and the fractal dimension of the backbone $D_b=1.78\mathrm{}\pm 0.02$. The number of "critical bonds" (if you remove them rigidity is lost) on the backbone scales as $L^x$, with $x=0.85\mathrm{}\pm 0.05$. The Young's modulus is also calculated.