HUBBARD-LIKE MODELS IN HIGH SPATIAL DIMENSIONS

The present paper studies the properties of Hubbard-like models in hig h spatial dimensions D. in a first part the limit of infinite dimensio n and its main features i.e. i) the mapping onto a generalized atomic model with an additional auxiliary field and ii) the validity of the l ocal approximation for the self-energy - are worked out in a systemati c (1/D)-expansion. Since the hopping matrix elements have to be proper ly scaled with the dimension D, the (1/D)-expansion is also an expansi on in the hopping amplitude. Thus for small hopping the D --> infinity -limit may serve as a proper approximation for finite-dimensional syst ems. The second part of the paper adopts the hybridisation-perturbatio n theory of the single impurity Anderson model in order to construct a perturbation theory for the auxiliary field of the generalized atom w hich can also be interpreted as an expansion in the hopping amplitude. The non-crossing approximation (NCA) is used to study the antiferroma gnetic phase transition of the D --> infinity-Hubbard model in the cas e of half filling: the critical temperature, the antiferromagnetic ord er parameter and the free energy of the lattice system are calculated. The NCA-results are in quite good agreement with recent results from the imaginary-time discretisation method.