Abstract
We demonstrate that all Ising antiferromagnets with general spin S and arbitrary many-neighbour interactions in the maximum critical field have highly degenerate ground states accompanied with nonzero residual entropies. For finite S, the residual entropies vanish when the range of interaction tends to infinity. The proof is realised by establishing bounds for residual entropies in the case of an Ising system situated on a lattice with arbitrary number of dimensions. In addition we estimate the ground-state entropies for a few two-dimensional lattices.
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