Thermodynamics of the 3D Hubbard model on approach to the Neel transition

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the N{\'e}el temperature using cluster dynamical mean-field theory. In particular we calculate the energy, entropy, density, double occupancy and nearest-neighbor spin correlations as a function of chemical potential, temperature and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle $S/N \approx 0.65(6)$ at $U/t = 8$ is sufficient to achieve a N{\'e}el state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.