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
相关论文
共 50 条
  • [31] Gap at 1 for the percolation threshold of Cayley graphs
    Panagiotis, Christoforos
    Severo, Franco
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2023, 59 (03): : 1248 - 1258
  • [32] SUFFICIENT CONDITIONS FOR SOME HAMILTONIAN PROPERTIES AND K-CONNECTIVITY OF GRAPHS
    Li, Rao
    JOURNAL OF APPLIED MATHEMATICS & INFORMATICS, 2016, 34 (3-4): : 221 - 225
  • [33] Some sufficient conditions for graphs being k-leaf-connected✩
    Wu, Jiadong
    Xue, Yisai
    Kang, Liying
    DISCRETE APPLIED MATHEMATICS, 2023, 339 : 11 - 20
  • [34] Some sufficient conditions for 1-planar graphs to be Class 1
    Zhang, Wenwen
    Wu, Jian-Liang
    THEORETICAL COMPUTER SCIENCE, 2015, 566 : 50 - 58
  • [35] INFINITE FAMILIES OF NONTRIVIAL TRIVALENT GRAPHS WHICH ARE NOT TAIT COLORABLE
    ISAACS, R
    AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (03): : 221 - 239
  • [36] Bond percolation on isoradial graphs: criticality and universality
    Geoffrey R. Grimmett
    Ioan Manolescu
    Probability Theory and Related Fields, 2014, 159 : 273 - 327
  • [37] Bond percolation on isoradial graphs: criticality and universality
    Grimmett, Geoffrey R.
    Manolescu, Ioan
    PROBABILITY THEORY AND RELATED FIELDS, 2014, 159 (1-2) : 273 - 327
  • [38] RIGOROUS BOUNDS ON THE BOND PERCOLATION THRESHOLD OF THE KAGOME
    OTTAVI, H
    JOURNAL DE PHYSIQUE, 1979, 40 (03): : 233 - 237
  • [39] Determination of the bond percolation threshold for the Kagome lattice
    Ziff, RM
    Suding, PN
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1997, 30 (15): : 5351 - 5359
  • [40] TEST OF SCALING NEAR BOND PERCOLATION THRESHOLD
    NAKANISHI, H
    STANLEY, HE
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1978, 11 (08): : L189 - L197
12345