  The interplay of disorder and strong correlations in quantum many-body
systems remains an open question. That is despite much progress made in recent
years with ultracold atoms in optical lattices to better understand phenomena
such as many-body localization or the effect of disorder on Mott
metal-insulator transitions. Here, we utilize the numerical linked-cluster
expansion technique, extended to treat disordered quantum lattice models, and
study exact thermodynamic properties of the disordered Fermi-Hubbard model on
the square and cubic geometries. We consider box distributions for the disorder
in the onsite energy, the interaction strength, as well as the hopping
amplitude and explore how energy, double occupancy, entropy, heat capacity and
magnetic correlations of the system in the thermodynamic limit evolve as the
strength of disorder changes. We compare our findings with those obtained from
determinant quantum Monte Carlo simulations and discuss the relevance of our
results to experiments with cold fermionic atoms in optical lattices.
