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

By means of the dynamical vertex approximation (DΓA) 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 Néel temperature (T N) by ∼30% for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between DΓA and DMFT in different regions of the phase diagram. © 2011 American Physical Society.We thank E. Gull and S. Fuchs for discussions and exchanging data. We acknowledge financial support from the EU-India network MONAMI (G. R.), Austria-Russia FWF project I 610-N16 (A. T.), RFBR Grants No. 10-02-91003-ANF_a, No. 11-02-00937-a, and Max-Planck associated partner group (A. K.), and FWF SFB ViCoM F4103-N13 (K. H.). Calculations were done on the Vienna Scientific Cluster