82 citations · 513 across the 21 of their papers we have counts for
7 papers · 1 filter
The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices
Robert M. Ziff, Christian R. Scullard, John C. Wierman +1
We give a conditional derivation of the inhomogeneous critical percolation manifold of the bow-tie lattice with five different probabilities, a problem that does not appear at firs…
The percolation critical polynomial as a graph invariant
Christian R. Scullard
Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work…
Polynomial sequences for bond percolation critical thresholds
Christian R. Scullard
In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4,6,12) and (3^4,6) lattices using the linearity approximation described in (Scullard…
Critical surfaces for general bond percolation problems
Christian R. Scullard, Robert M. Ziff
We present a general method for predicting bond percolation thresholds and critical surfaces for a broad class of two-dimensional periodic lattices, reproducing many known exact re…
Exact bond percolation thresholds in two dimensions
Robert M. Ziff, Christian R. Scullard
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classe…
Predictions of bond percolation thresholds for the kagomé and Archimedean lattices
Christian R. Scullard, Robert M. Ziff
Here we show how the recent exact determination of the bond percolation threshold for the martini lattice can be used to provide approximations to the unsolved kagomé and (3,12^2)…