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We study thermodynamics of the 3D Hubbard model at half filling on approachto the N\'eel transition by means of large-scale unbiased DiagrammaticDeterminant Monte Carlo simulations. We obtain the transition temperature inthe strongly correlated regime, as well as temperature dependence of energy,entropy, double occupancy, and the nearest-neighbor spin correlation function.Our results improve the accuracy of previous unbiased studies and presentaccurate benchmarks in the ongoing effort to realize the antiferromagneticstate of matter with ultracold atoms in optical lattices.

N\'eel temperature and thermodynamics of the half-filled 3D Hubbard model by Diagrammatic Determinant Monte Carlo