A duality theorem for planar three-body Ising models and their vertex model equivalences

Publisher Website
Google Scholar
Abstract
A duality theorem is proved which establishes the property of self-duality in the thermodynamic limit to be a natural property of a large class of pure three-body Ising models. A new form of low temperature expansion is obtained for triplet Ising models in zero field, which are closed polygon expansions and are highly lattice dependent. These closed polygon expansions readily establish an equivalence between pure triplet models and corresponding vertex models, and it is seen that a number of 'ice rules' are equivalent to triplet models at the dual point.