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 system, such as the Hubbard model and the periodic Anderson model. Many investigations which are prohibitively difficult in finite dimensions, become tractable in d = infinity. At the same time essential features of systems in d = 3 and even lower dimesions are very well described by the results obtained in d = infinity. 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.