Soluble extension of the Ising model

In this note we wish to relate a somewhat trivial, but surprising, soluble extension of the multidimensional Ising model. Our extension was motivated by recent experiments on a real material, dysprosium aluminum garnet (DyAlG), which closely resembles an ideal three-dimensional Ising model,1 except for what appeared to be one unfortunate detail: The electronic (Ising) spins are connected not just to their electronic neighbors, but also to their own dysprosium nuclei by a fairly large hyperfine interaction.