Elastic Backbone Defines a New Transition in the Percolation Model

Physical Review Letters
Cesar I N Sampaio FilhoAndré A Moreira

Abstract

The elastic backbone is the set of all shortest paths. We found a new phase transition at p_{eb} above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in 2D, its fractal dimension is 1.750±0.003, and one obtains a novel set of critical exponents β_{eb}=0.50±0.02, γ_{eb}=1.97±0.05, and ν_{eb}=2.00±0.02, fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities p_{eb} for the triangular and tilted square lattice for site and bond percolation. This transition describes a sudden rigidification as a function of density when stretching a damaged tissue.

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Citations

Sep 17, 2019·Physical Review Letters·Kenji Harada, Naoki Kawashima
Aug 17, 2020·Physical Review. E·Zhipeng Xun, Robert M Ziff
Nov 28, 2019·Physical Review. E·M N NajafiH J Herrmann
Jul 22, 2020·Physical Review. E·S S Manna, Robert M Ziff

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