Efficient calculation of the antiferromagnetic phase diagram of the three-dimensional Hubbard model

The dynamical cluster approximation (DCA) with Betts clusters is used to calculate the antiferromagnetic phase diagram of the three-dimensional Hubbard model at half-filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt [Eur. Phys. J. B 17, 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000.