D--dimensional half--filled Hubbard model. Zero temperature paramagnetic solution

Abstract

In this paper we investigate effects of a lattice dimension on strongly correlated electronic systems at $T=0 K$. The model for numerical calculations is formalized in terms of the integral equations which were obtained previously for the half -- filled paramagnetic Hubbard model. The assumption that all relevant functions of the system have a magnitude dependence of momentus vectors makes ultimately possible treating a lattice dimension $D$ as an external parameter. We here submit for consideration the number of doubly occupied lattice sites, the electronic density of states, and the momentum distribution in electronic occupation numbers at $D$=1, $D$=2, $D$=3