Rigidity of random networks of stiff fibers in the low-density limit

Rigidity percolation is analyzed in two-dimensional random networks of stiff fibers. As fibers are randomly added to the system there exists a density threshold ${q=q}_{\min }$ above which a rigid stress-bearing percolation cluster appears. This threshold is found to be above the connectivity percolation threshold ${q=q}_c$ such that $q_{\min }=(1.1698\mathrm{}\pm {0.0004)q}_c.$ The transition is found to be continuous, and in the universality class of the two-dimensional central-force rigidity percolation on lattices. At percolation threshold the rigid backbone of the percolating cluster was found to break into rigid clusters, whose number diverges in the limit of infinite system size, when a critical bond is removed. The scaling with system size of the average size of these clusters was found to give a new scaling exponent $\delta =1.61\mathrm{}\pm \mathrm{0.04.}$