  I review computational studies of different models of elastic network
self-organization leading to the existence of a globally isostatic (rigid but
unstressed) or nearly isostatic intermediate phase. A common feature of all
models considered here is that only the topology of the elastic network is
taken into account; this allows the use of an extremely efficient constraint
counting algorithm, the pebble game. In models with bond insertion without
equilibration, the intermediate phase is rigid with probability one but
stress-free; in models with equilibration, the network in the intermediate
phase is maintained in a self-organized critical state on the verge of
rigidity, fluctuating between percolating and nonpercolating but remaining
nearly isostatic. I also consider the connectivity analogs of these models,
some of which correspond to well-studied cases of loopless percolation and
where another kind of intermediate phase, with existing but nonpercolating
stress, was studied.
