Scaling for the Percolation Backbone

Details Scaling for the Percolation Backbone Scaling for the Percolation Backbone

1999-04-05

arxiv.org/abs/cond-mat/9904062v1

Phys. Rev. E (Rapid Comm.) 60, R1123 (1999)

Physics

Condensed Matter

Statistical Mechanics

3 pages, 5 postscript figures, Latex/Revtex/multicols/epsf

Scientific paper

10.1103/PhysRevE.60.R1123

We study the backbone connecting two given sites of a two-dimensional lattice separated by an arbitrary distance $r$ in a system of size $L$. We find a scaling form for the average backbone mass: $\sim L^{d_B}G(r/L)$, where $G$ can be well approximated by a power law for $0\le x\le 1$: $G(x)\sim x^{\psi}$ with $\psi=0.37\pm 0.02$. This result implies that $ \sim L^{d_B-\psi}r^{\psi}$ for the entire range $0

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