Rigidity Loss in Disordered Systems: Three Scenarios
  We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings. 
Wouter G. Ellenbroek, Varda F. Hagh, Avishek Kumar, M. F. Thorpe,   Martin van Hecke
cond-mat.soft cond-mat.dis-nn cond-mat.stat-mech