title: Criteria for evaluation of universal formulas for percolation thresholds.
abstract: Several universal formulas that predict approximate values for percolation thresholds of all periodic graphs have been proposed in the physics and engineering literature. The existing universal formulas have been found to have substantial errors in their predictions for some lattices. This paper proposes a set of desirable criteria for universal formulas to satisfy, and investigates which criteria are satisfied by two bond threshold formulas and two site threshold formulas most cited in the literature. The analysis is limited to lattices in two dimensions.
authors.affiliation: Mathematical Sciences Department, 104 Whitehead Hall, Johns Hopkins University, Baltimore, MD 21218, USA.
authors.forename: John C
authors.initials: JC
authors.lastname: Wierman
authors.forename: Dora Passen
authors.initials: DP
authors.lastname: Naor