2008/12/31 by Robert M. Ziff, Hang Gu · 32 citations
Mathematics · Physics and Astronomy · #Combinatorics #Criticality #Electrical resistivity and conductivity #Lattice (music) #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Upper and lower bounds #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.020102
published in Physical Review E 79(2), 020102 (American Physical Society) · Several new figures and small changes
arxiv created 2009/01/13 · openalex publication_date 2009/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Lattices that can be represented in a kagomé-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P3 , the probability that all three vertices in the triangle connect, and P0 , the probability that none connect. A linear approximation for P3(P0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numerically determined relation for P3(P0) gives thresholds for the kagomé, site-bond honeycomb, (3-12;2) lattice, and "stack-of-triangle" lattices that compare favorably with numerical results.