  Recent experimental results for covalent glasses suggest the existence of an
intermediate phase attributed to the self-organization of the glass network
resulting from the tendency to minimize its internal stress. However, the exact
nature of this experimentally measured phase remains unclear. We modify a
previously proposed model of self-organization by generating a uniform sampling
of stress-free networks. In our model, studied on a diluted triangular lattice,
an unusual intermediate phase appears, in which both rigid and floppy networks
have a chance to occur, a result also observed in a related model on a Bethe
lattice by Barre et al. [Phys. Rev. Lett. 94, 208701 (2005)]. Our results for
the bond-configurational entropy of self-organized networks, which turns out to
be only about 2% lower than that of random networks, suggest that a
self-organized intermediate phase could be common in systems near the rigidity
percolation threshold.
