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Using the Wick theorem for Hubbard operators, we generate the linked-cluster expansion around the atomic limit of the Hubbard model and use it to calculate the free energy, and the uniform and the staggered magnetic susceptibility up to the fourth order. We have checked all existing controversial results on this problem and found out that our results agree with those of K.-K. Pan and Y.-L. Wang [Phys. Rev. B 43, 370 (1991)], which were derived with an entirely different method.
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