  We study the 3D Hubbard model with anisotropic nearest neighbor tunneling
amplitudes using the dynamical cluster approximation and compare the results
with a quantum simulation experiment using ultracold fermions in an optical
lattice, focussing on magnetic correlations. We find that the short-range spin
correlations are significantly enhanced in the direction with stronger
tunneling amplitudes. Our results agree with the experimental observations and
show that the experimental temperature is lower than the strong tunneling
amplitude. We characterize the system by examining the spin correlations beyond
neighboring sites and determine the distribution of density, entropy and spin
correlation in the trapped system. We furthermore investigate the dependence of
the critical entropy at the N\'eel transition on anisotropy.
