Magnetic properties of the three-dimensional Hubbard model at half filling

We study the magnetic properties of the three-dimensional (3D) Hubbard model at half filling in the two particle self-consistent formalism, previously developed for the 2D model. We focus on the Neel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with dynamical mean-field (DMF) results for the isotropic 3D model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3D case, and the 2D or anisotropic 3D cases for the double occupation factor. Even for this local correlation function, 2D or anisotropic 3D cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.