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

Tomoaki Nogawa; Takehisa Hasegawa

doi:10.1088/1751-8113/42/14/145001

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

Tomoaki Nogawa, Takehisa Hasegawa

INF - Applied Information Sciences

Research output: Contribution to journal › Article › peer-review

31 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 p_c1 and p_c2. The mean cluster size diverges as p approaches p_c1 from below. The system is critical at all the points in the intermediate phase (p_c1 < p < p_c2) and there exist infinitely many infinite clusters. In this phase, the corresponding fractal exponent continuously increases with p from zero to unity. Above p_c2 the system has a unique infinite cluster.

Original language	English
Article number	145001
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	42
Issue number	14
DOIs	https://doi.org/10.1088/1751-8113/42/14/145001
Publication status	Published - 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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10.1088/1751-8113/42/14/145001

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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.",

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AB - 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.

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

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