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
-
The Système International de Référence and its application in key comparisons
Guy Ratel 2007 Metrologia 44 S7
-
Polyhedral oligomeric silsequioxane monolayer as a nanoporous interlayer for preparation of low-k dielectric films
Ying-Ling Liu et al 2007 Nanotechnology 18 225701
-
Solitons in the Higgs phase: the moduli matrix approach
Minoru Eto et al 2006 J. Phys. A: Math. Gen. 39 R315
-
Properties of the volume operator in loop quantum gravity: II. Detailed presentation
Johannes Brunnemann and David Rideout 2008 Class. Quantum Grav. 25 065002
-
FOCUS ON QUANTUM CRYPTOGRAPHY: THEORY AND PRACTICE
N Lütkenhaus and A J Shields 2009 New J. Phys. 11 045005
-
The SECOQC quantum key distribution network in Vienna
M Peev et al 2009 New J. Phys. 11 075001
-
Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
Kazuhiro Yokota et al 2009 New J. Phys. 11 033011
-
Bilateral comparison of 10 V standards between the NML (Ireland) and the BIPM, May to June 2008 (part of the ongoing BIPM key comparison BIPM.EM-K11.b)
O Power et al 2008 Metrologia 45 01008
-
Final report of the on-going key comparison BIPM.QM-K1: Ozone at ambient level, comparison with VNIIM, 2007
Joële Viallon et al 2008 Metrologia 45 08009
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