Near-equalities for some two-dimensional Ising-model correlation ratios

Abstract

The i–δ relations and the criticality condition, which are used in recent theoretical calculations of the Ising-model transition temperature and critical exponent η, are tested against exact calculations for the two-dimensional lattices: square, plane triangular, and honeycomb. They are found to be valid to within 2%. They are also tested against series results for the three-dimensional hydrogen peroxide lattice, with which they are shown to be consistent to within 3.3%. A new derivation is given of the i–δ relations.