Infinite graphs with a nontrivial bond percolation threshold: Some sufficient conditions

被引：7
|
作者：
Procacci, A
Scoppola, B
机构：
[1] Univ Fed Minas Gerais, Dept Matemat, BR-30161970 Belo Horizonte, MG, Brazil
[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
来源：
JOURNAL OF STATISTICAL PHYSICS | 2004年 / 115卷 / 3-4期
关键词：
percolation; infinite graphs; Peierls argument;
D O I：
10.1023/B:JOSS.0000022369.76414.33
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider Bernoulli bond percolation on infinite graphs and we identify a class of graphs for which the critical percolation probability is strictly less than 1. The graphs in this class have to fulfill conditions stated in terms of a minimal cut set property and a logarithmic isoperimetric inequality. For the particular case of planar graphs the condition on minimal cut sets can be be replaced by the assumption that the dual of the graph is bounded degree.
引用
收藏
页码：1113 / 1127
页数：15
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