2011/01/08 by Seung Ki Baek, Petter Minnhagen
Mathematics · Physics and Astronomy · Psychology · #Binary number #Binary tree #Bounded function #Combinatorics #Directed percolation #Discrete mathematics #Duality (order theory) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation threshold #Physics #Psychology #Quantum mechanics #Renormalization group #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Transitive relation #Tree (set theory) #Upper and lower bounds #cond-mat.stat-mech
paper · pdf · doi:10.1016/j.physa.2010.12.030
published as Physica A 390, 1447 (2011) · 12 pages, 15 figures
openalex publication_date 2011/01/08 · arxiv created 2011/02/16 · arxiv updated 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By studying its subgraphs, it is argued that the lower critical percolation threshold of the enhanced binary tree (EBT) is bounded as pc1 < 0.355059, while the upper threshold is bounded both from above and below by 1/2 according to renormalization-group arguments. We also review a correlation analysis in an earlier work, which claimed a significantly higher estimate of pc2 than 1/2, to show that this analysis in fact gives a consistent result with this bound. Our result confirms that the duality relation between critical thresholds does not hold exactly for the EBT and its dual, possibly due to the lack of transitivity.