Percolation and jamming in random bond deposition

A model is presented in which on the bonds of a square lattice linear segments (“needles”) of a constant length a are randomly placed. We investigate the dependence of the percolation and jamming thresholds on the length of the needles. The difference from the standard site deposition problem is demonstrated. We show that the system undergoes a transition at a=6. When shorter needles are used, the system first becomes percolating before becoming jammed. For longer needles the lattice becomes jammed but there is no percolation. We present evidence that the transition is due to different clustering of the short and long needles. We also determine the Fisher exponent, obtaining the same value as for standard two-dimensional percolation.