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Antiferromagnetic spin models in two dimensions with known ground states.

Some frustrated spin models in two dimension are constructed, the ground state of which can be determined exactly in certain regimes of the coupling parameter space. The Hamiltonians describing the models contain inhomogeneous spin-spin couplings of at most five types: nearest-neighbor, diagonal, next-nearest-neighbor, knight's-move-distance-away, and further-neighbor-diagonal. The possible ground states include columnar, staggered, and herringbone dimer states, the resonating-valence-bond state, and other dimer states.