model is mapped onto the two-site SIAM (\[eq:siam2\]) by means a strongly simplified self-consistency condition. As compared to the two-site DMFT, the present self-energy-functional approach not only represents a clear conceptual improvement but also improves the actual results for $z(U)$ and for $U_{\rm c}$ (see Fig. \[fig:zofu\] and note that $U_{\rm c}=6$ within the linearized DMFT, $U_{\rm c}=5.8450$ within the DIA for $n_{\rm s}=2$, and $U_{\rm c} = 5.84$ and $U_{\rm c} = 5.88$ from numerical evaluations [@MSK+95; @Bul99] of the full DMFT).

The self-energy-functional approach with reference system of Fig. 1c and small $n_{\rm s}$ actually represents a new variant of the DMFT-exact-diagonalization method (ED). [@CK94; @SRKR94] As compared to previous formulations of the ED, the convergence with respect to $n_{\rm s}$ appears to be faster: Compare the results for $n_{\rm s}=2$, $n_{\rm s}=4$ and $n_{\rm s}=\infty$ (full DMFT) in Fig. \[fig:zofu\] with those of Ref. . More important, however, there is no need for a fit procedure in the present approach; any arbitrariness in the method to find the SIAM parameters is avoided completely. Furthermore, consistent results will be obtained for any finite $n_{\rm s}$ while in the usual ED this can be expected in the DMFT limit 