title: Accuracy of universal formulas for percolation thresholds based on dimension and coordination number.
abstract: Recent mathematical results regarding percolation thresholds are relevant to efforts to find universal formulas for the percolation threshold. This Brief Report uses exact solutions and recent rigorous bounds for site and bond percolation thresholds to demonstrate that any universal formula based on only the dimension and the coordination number must provide estimates differing substantially from the true threshold value for some lattices.
authors.affiliation: Mathematical Sciences Department, 104 Whitehead Hall, Johns Hopkins University, Baltimore, Maryland 21218, USA.
authors.forename: John C
authors.initials: JC
authors.lastname: Wierman