Infinite-cluster geometry in central-force networks
Statistical Mechanics
2016-08-31 v1 Materials Science
Computational Physics
Abstract
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.
Cite
@article{arxiv.cond-mat/9612239,
title = {Infinite-cluster geometry in central-force networks},
author = {Cristian F. Moukarzel and Phillip M. Duxbury and P. L. Leath},
journal= {arXiv preprint arXiv:cond-mat/9612239},
year = {2016}
}
Comments
6 pages, 4 figures, uses epsfig. Accepted for publication in Physical Review Letters