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The sequence-transformation method due to Vanden Broeck and Schwartz is used to accelerate the convergence of numerical finite-lattice data on ground-state energies to their infinite-lattice limit. Highly accurate estimates of the ground-state energy are obtained for the S=1/2 antiferromagnetic Heisenberg and XY rings. The ground-state energy of the $S=1$ antiferromagnetic Heisenberg ring is also estimated accurately.
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Hiroshi Betsuyaku (1986) studied this question.
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