Critical Properties of the Half-Filled Hubbard Model in Three Dimensions

By means of the dynamical vertex approximation (D Gamma A) we include spatial correlations on all length scales beyond the dynamical mean-field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to nonlocal fluctuations are (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti) ferromagnet and (ii) a sizable reduction of the Neel temperature (T-N) by similar to 30% for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between D Gamma A and DMFT in different regions of the phase diagram.