Seung Ki Baek et al 2009 J. Phys. A: Math. Theor. 42 478001 doi:10.1088/1751-8113/42/47/478001
Comment on 'Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'
Seung Ki Baek1, Petter Minnhagen1 and Beom Jun Kim2
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The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds pc1 and pc2 with pc1 < pc2. Our Monte Carlo study implies that the second threshold pc2 is significantly lower than a recent claim by Nogawa and Hasegawa (2009 J. Phys. A: Math. Theor. 42 145001). This means that pc2 for the EBT does not obey the duality relation for the thresholds of dual graphs 
which is a property of a transitive, nonamenable, planar graph with one end. As in regular hyperbolic lattices, this relation instead becomes an inequality 
. We also find that the critical behavior is well described by the scaling form previously found for regular hyperbolic lattices.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
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82B26 Phase transitions (general)
82B43 Percolation (See also 60K35)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
- Subjects
- Dates
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Issue 47 (27 November 2009)
Received 8 May 2009
Published 4 November 2009
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Comment on 'Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees'
Seung Ki Baek et al 2009 J. Phys. A: Math. Theor. 42 478001
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