Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees

Tomoaki Nogawa, Takehisa Hasegawa

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We perform Monte Carlo simulations to study the Bernoulli (p) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two distinct percolation thresholds pc1 and pc2. The mean cluster size diverges as p approaches pc1 from below. The system is critical at all the points in the intermediate phase (pc1 < p < pc2) and there exist infinitely many infinite clusters. In this phase, the corresponding fractal exponent continuously increases with p from zero to unity. Above pc2 the system has a unique infinite cluster.

Original languageEnglish
Article number145001
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number14
DOIs
Publication statusPublished - 2009 Jul 24

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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