2005/10/10 by Robert M. Ziff, Ziff, Robert M.
Materials Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.cond-mat/0510245
openalex publication_date 2005/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suggested by Scullard's recent star-triangle relation for bond correlated\nsystems, we propose a general "cell/dual-cell" transformation, which allows in\nprinciple an infinite variety of lattices with exact percolation thresholds to\nbe generated. We directly verify Scullard's new site percolation thresholds,\nand derive the bond thresholds for his "martini" lattice (pc = 1/sqrt(2)) and\nthe "A" lattice (pc = 0.625457..., solution to p5 - 4 p4 + 3 p3 + 2 p2 - 1\n= 0). We also present a precise Monte-Carlo test the site threshold for the "A"\nlattice.\n