Universal condition for critical percolation thresholds of kagome-like lattices
Disordered Systems and Neural Networks
2009-11-13 v2 Statistical Mechanics
Abstract
Lattices that can be represented in a kagome-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P_3, the probability that all three vertices in the triangle connect, and P_0, the probability that none connect. A linear approximation for P_3(P_0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numerically determined relation for P_3(P_0) gives thresholds for the kagome, site-bond honeycomb, (3-12^2), and "stack-of-triangle" lattices that compare favorably with numerical results.
Keywords
Cite
@article{arxiv.0812.0181,
title = {Universal condition for critical percolation thresholds of kagome-like lattices},
author = {Robert M. Ziff and Hang Gu},
journal= {arXiv preprint arXiv:0812.0181},
year = {2009}
}
Comments
Several new figures and small changes