Exact Critical Percolation Probabilities for Site and Bond Problems in Two Dimensions
M. F. Sykes, J. W. Essam
Source abstract
An exact method for determining the critical percolation probability, pc, for a number of two-dimensional site and bond problems is described. For the site problem on the plane triangular lattice pc = ½. For the bond problem on the triangular, simple quadratic, and honeycomb lattices, pc=2 sin (118π),12,1−2 sin (118π), respectively. A matching theorem for the mean number of finite clusters on certain two-dimensional lattices, somewhat analogous to the duality transformation for the partition function of the Ising model, is described.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.