  We show how the Hintermann-Merlini-Baxter-Wu model (which is a generalization
of the well-known Baxter-Wu model to a general Eulerian triangulation) can be
mapped onto a particular infinite-coupling-limit of the Ashkin-Teller model. We
work out some mappings among these models, also including the standard and
mixed Ashkin-Teller models. Finally, we compute the phase diagram of the
infinite-coupling-limit Ashkin-Teller model on the square, triangular,
hexagonal, and kagome lattices.
