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We verify signatures of antiferromagnetic (AF) correlations in the doubleoccupancy D [Gorelik et al., PRL 105, 065301 (2010)] and study theirdimensional dependence using direct quantum Monte Carlo in dimensions d=2,3 andBethe Ansatz in d=1. We find quantitative agreement with dynamical mean-fieldtheory (DMFT) in the cubic case and qualitative agreement down to d=1. As afunction of entropy s=S/(N k_B), D is nearly universal with respect to d; theminimum in D(s) approaches s=log(2) at strong coupling, as predicted by DMFT.Long-range order appears hardly relevant for the current search of AFsignatures in cold fermions. Thus, experimentalists need not achieve s<log(2)/2and should consider lower dimensions, for which the AF effects are larger.

Double occupancy as a universal probe for antiferromagnetic correlations and entropy in cold fermions on optical lattices