  In this work we study zero-temperature phases of the anisotropic Hubbard
model on a three-dimensional cubic lattice in a weak coupling regime. It is
known that, at half-filling, the ground state of this model is
antiferromagnetic (commensurate spin-density wave). For non-zero doping,
various types of spatially inhomogeneous phases, such as phase-separated states
and the state with domain walls ("soliton lattice"), can emerge. Using the
mean-field theory, we evaluate the free energies of these phases to determine
which of them could become the true ground state in the limit of small doping.
Our study demonstrates that the free energies of all discussed states are very
close to each other. Smallness of these energy differences suggests that, for a
real material, numerous factors, unaccounted by the model, may arbitrary shift
the relative stability of the competing phases. This further implies that
purely theoretical prediction of the true ground state in a particular
many-fermion system is unreliable.
