  We examine the nature of the transition to the antiferromagnetically ordered
state in the half-filled three-dimensional Hubbard model using the dual-fermion
multiscale approach. Consistent with analytics, in the weak-coupling regime we
find that spin-flip excitations across the Fermi surface are important, and
that the strong coupling regime is described by Heisenberg physics. In the
intermediate interaction, strong correlation regime we find aspects of both
local and non-local correlations. We analyze the critical exponents of the
transition in the strong coupling regime and find them to be consistent with
Heisenberg physics down to an interaction of $U/t=10$.
