Infinite-cluster geometry in central-force networks
Cristian F. Moukarzel, Phillip M. Duxbury, P. L. Leath
Abstract
We show that the infinite percolating cluster (with density Pinf) of central-force networks is composed of: a fractal stress-bearing backbone (Pb) and; rigid but unstressed ``dangling ends'' which occupy a finite volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is then a first-order transition in Pinf = Pd + Pb, while Pb is second-order with exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations of triangular lattices give Beta'tr = 0.255 +/- 0.03.
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