Phase diagram of the half-filled 3D Hubbard model

The antiferromagnetic Neél temperature $T_N$ is calculated as a function of the Coulomb interaction U for a half-filled 3D Hubbard model. Numerical results are given for the specific heat and staggered magnetic suspectibility on periodic lattices ranging from $4^3$–${10}^3$ sites, and used to determine $T_N$. The size dependence of the results suggests that the transition is weakly first order at small to intermediate values of U.