  We determine antiferromagnetic (AF) signatures in the half-filled Hubbard
model at strong coupling on a cubic lattice and in lower dimensions. Upon
cooling, the transition from the charge-excitation regime to the AF Heisenberg
regime is signaled by a universal minimum of the double occupancy at entropy
s=S/(N k_B)=s*=ln(2) per particle and a linear increase of the next-nearest
neighbor (NNN) spin correlation function for s<s*. This crossover, driven by a
gain in kinetic exchange energy, appears as the essential AF physics relevant
for current cold-atom experiments. The onset of long-range AF order (at low s
on cubic lattices) is hardly visible in nearest-neighbor spin correlations
versus s, but could be detected in spin correlations at or beyond NNN
distances.
