High dimensions - a new approach to fermionic lattice models

The limit of high spatial dimensions d, which is well-established in the theory of classical and localized spin models, is shown to be a fruitful approach also to itinerant fermion systems, such as the Hubbard model and the periodic Anderson model. Many investigations which are probability difficult in finite dimensions, become tractable in d=∞. At the same time essential features of systems in d=3 and even lower dimensions are very well described by the results obtained in d=∞. A wide range of applications of this new concept (e.g., in perturbation theory, Fermi liquid theory, variational approaches, exact results, etc.) is discussed and the state-of-the-art is reviewed. (orig.)