PMID: 22587034May 17, 2012Paper

Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
K J SchrenkH J Herrmann

Abstract

The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms, 25, 432 (2004)], and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett. 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimensions, the clusters at the threshold are compact with a fractal surface of fractal dimension d(f)=1.49±0.02. On the simple-cubic lattice, distinct jumps in the size of the largest cluster are observed. We proceed to analyze the tree-like version of the model, where only merging bonds are sampled, for dimension two to seven. The transition is again discontinuous in any considered dimension. Finally, the dependence of the cluster-size distribution at the threshold on the spatial dimension is also investigated.

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Citations

Oct 23, 2012·Scientific Reports·K J SchrenkH J Herrmann
Jul 28, 2013·Nature Communications·Malte SchröderJan Nagler
Jan 20, 2018·Physical Review. E·Malte SchröderJan Nagler
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May 14, 2016·Physical Review. E·L BöttcherH J Herrmann
Nov 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wei ChenJan Nagler
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yang ZhangZhiming Zheng
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L Cao, J M Schwarz
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yang ZhangZhiming Zheng
May 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R A da CostaJ F F Mendes
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Woosik ChoiYup Kim
Sep 13, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R A da CostaJ F F Mendes
Dec 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K J SchrenkH J Herrmann
Jun 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wei ChenRaissa M D'Souza
Apr 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Seongmin KimB Kahng
May 3, 2014·Physical Review Letters·Wei ChenJan Nagler
Aug 21, 2021·Physical Review. E·Yejun Kang, Young Sul Cho

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