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In this work we study zero-temperature phases of the anisotropic Hubbardmodel on a three-dimensional cubic lattice in a weak coupling regime. It isknown that, at half-filling, the ground state of this model isantiferromagnetic (commensurate spin-density wave). For non-zero doping,various types of spatially inhomogeneous phases, such as phase-separated statesand the state with domain walls ("soliton lattice"), can emerge. Using themean-field theory, we evaluate the free energies of these phases to determinewhich 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 veryclose to each other. Smallness of these energy differences suggests that, for areal material, numerous factors, unaccounted by the model, may arbitrary shiftthe relative stability of the competing phases. This further implies thatpurely theoretical prediction of the true ground state in a particularmany-fermion system is unreliable.

Competition of spatially inhomogeneous states in antiferromagnetic Hubbard model