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 language | English |
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Article number | 145001 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 42 |
Issue number | 14 |
DOIs | |
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)