A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.