Infinite-cluster geometry in central-force networks

We show that the infinite percolating cluster (with density P-proportional to) of central-force networks is composed of a fractal stress-bearing backbone (P-B) and rigid but unstressed ''isostatic ends'' which occupy a finite volume fraction of the lattice (P-1). Near the rigidity threshold p* there is then a first-order transition in P-infinity = P-1 + P-B, while P-B is second order with exponent beta'. A new mean-field theory suggests beta(mf)' = 1/2, while simulations of triangular lattices give beta(t)' = 0.25 +/- 0.03.