Ordinary percolation with discontinuous transitions

被引：86
作者：
Boettcher, Stefan [1 ]
Singh, Vijay [1 ]
Ziff, Robert M. [2 ,3 ]
机构：
[1] Emory Univ, Dept Phys, Atlanta, GA 30322 USA
[2] Univ Michigan, Ctr Study Complex Syst, Ann Arbor, MI 48109 USA
[3] Univ Michigan, Dept Chem Engn, Ann Arbor, MI 48109 USA
来源：
NATURE COMMUNICATIONS | 2012年 / 3卷
基金：
美国国家科学基金会;
关键词：
EXPLOSIVE PERCOLATION;
D O I：
10.1038/ncomms1774
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
Percolation on a one-dimensional lattice and fractals, such as the Sierpinski gasket, is typically considered to be trivial, because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a non-trivial critical point. There, the usual order parameter, describing the probability of any node to be part of the largest cluster, jumps instantly to a finite value. Here we provide a simple example in the form of a small-world network consisting of a one-dimensional lattice which, when combined with a hierarchy of long-range bonds, reveals many features of this transition in a mathematically rigorous manner.
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页数：5
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