Stressed backbone and elasticity of random central-force systems

TL;DR

This paper introduces a new algorithm to analyze the stress backbone and elasticity of large, randomly displaced triangular lattices, providing detailed critical exponents and mechanical properties relevant to disordered systems.

Contribution

A novel algorithm for identifying the stress backbone in large, randomly displaced lattices and detailed measurements of critical exponents and elastic properties.

Findings

Percolation threshold Pc=0.6975 +/- 0.0003

Correlation length exponent ν=1.16 +/- 0.03

Fractal dimension of the backbone Db=1.78 +/- 0.02

Abstract

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 Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =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 L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.