Tomoaki Nogawa and Takehisa Hasegawa 2009 J. Phys. A: Math. Theor. 42 145001 doi:10.1088/1751-8113/42/14/145001
Tomoaki Nogawa1 and Takehisa Hasegawa2
Show affiliationsWe 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.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
02.10.Ox Combinatorics; graph theory
64.60.A- Specific approaches applied to studies of phase transitions
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B43 Percolation (See also 60K35)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 14 (10 April 2009)
Received 1 December 2008, in final form 9 February 2009
Published 16 March 2009
Tomoaki Nogawa and Takehisa Hasegawa 2009 J. Phys. A: Math. Theor. 42 145001
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