Stressed backbone and elasticity of random central-force systems
Cristian F. Moukarzel, Phillip M. Duxbury
Abstract
We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 106 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent ν=1.16 +/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number of ``critical bonds'' (if you remove them rigidity is lost) on the backbone scales as Lx, with x=0.85 +/- 0.05. The Young's modulus is also calculated.
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