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
Show affiliationsCOMMENTS AND REPLIES
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
-
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
-
82B26 Phase transitions (general)
82B43 Percolation (See also 60K35)
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
- Subjects
- Dates
-
Issue 47 (27 November 2009)
Received 8 May 2009
Published 4 November 2009
-
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
-
A Sensitive Scheme to Observe Weak Photo-Refraction Effects in Some Nonlinear Optical Crystals Pumped by Ultrashort Optical Pulses
Xu Shi-Xiang et al 2009 Chinese Phys. Lett. 26 114209
-
Spin Relaxation of Electrons in Single InAs Quantum Dots
Ma Shan-Shan et al 2009 Chinese Phys. Lett. 26 117201
-
Improved charge storage characteristics of the tetralayer non-volatile memory structure using nickel nanocrystal trapping layer
Debashis Panda et al 2009 Semicond. Sci. Technol. 24 115020
-
Effects of Grain Boundary Barrier in ZnO/Si Heterostructure
Liu Bing-Ce et al 2009 Chinese Phys. Lett. 26 117101
-
Shining X-rays on catalysts at work
J-D Grunwaldt 2009 J. Phys.: Conf. Ser. 190 012151
-
Kinetics of heterogeneous grain boundary precipitation of Ni3Al in nickel alloy
C Hin 2009 J. Phys. D: Appl. Phys. 42 225309
-
Structure of catalytically active gold nanoparticles by XAFS spectroscopy
S Erenburg et al 2009 J. Phys.: Conf. Ser. 190 012121
-
Phase-locking of an axisymmetric-fold combination cavity CO2 laser using the back surface of the output-mirror
Yonggen Xu et al 2009 J. Opt. A: Pure Appl. Opt. 11 125410
-
Analytically periodic solutions to the three-dimensional Euler–Poisson equations of gaseous stars with a negative cosmological constant
Manwai Yuen 2009 Class. Quantum Grav. 26 235011
Users also read
What's this?- Monte Carlo simulation study of the two-stage percolation transition in enhanced binary trees
- Discretely holomorphic parafermions and integrable loop models
- The collision of multimode dromions and a firewall in the two-component long-wave–short-wave resonance interaction equation
Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- Discrete breathers and the anomalous decay of luminescence