Infinite-cluster geometry in central-force networks

Details Infinite-cluster geometry in central-force networks Infinite-cluster geometry in central-force networks

1996-12-29

arxiv.org/abs/cond-mat/9612239v1

Phys. Rev. Lett. 78 (1997), 1486.

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures, uses epsfig. Accepted for publication in Physical Review Letters

Scientific paper

10.1103/PhysRevLett.78.1480

We show that the infinite percolating cluster (with density P_inf) 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 P_inf = 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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