Systematic $1/\mathit{d}$ Corrections to the Infinite-Dimensional Limit of Correlated Lattice Electron Models

We present a self-consistent treatment of Hubbard-like lattice models at large, but finite, spatial dimensions $d$. This involves a systematic expansion in powers of $1/d$ about the limit $d=\infty$. The first-order corrections can be obtained by self-consistent solution of coupled one- and two-impurity models. We calculate the leading corrections to properties of the Falicov-Kimball model. The infinite-dimensional limit seems to describe this particular model remarkably well even for $d=2\mathrm{}$.