Universal probes for antiferromagnetic correlations and entropy in cold   fermions on optical lattices
  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. 
E. V. Gorelik, D. Rost, T. Paiva, R. Scalettar, A. Kl\"umper, and N.   Bl\"umer
cond-mat.quant-gas cond-mat.str-el