Generalized Shastry-Sutherland models in three and higher dimensions

We construct Heisenberg antiferromagnetic models in arbitrary dimensions that have isotropic valence-bond crystals (VBC's) as their exact ground states. The d=2 model is the Shastry-Sutherland model. In the three-dimensional case we show that it is possible to have a lattice structure, analogous to that of SrCu2(BO3)(2), where the stronger bonds are associated with shorter bond lengths. A dimer mean-field theory becomes exact at d-->infinity and a systematic 1/d expansion can be developed about it. We study the Neel-VBC transition at large d and find that the transition is first order in even but second order in odd dimensions.