Converging bounds for the free energy in certain statistical mechanical problems

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Abstract
We present sequences of converging upper and lower bounds to the partition function per spin specifically for a ferromagnetic Ising model which are valid in the entire finite, magnetic-field, inverse-temperature plane. They are based on the exact high-temperature expansions for a finite system, properties of generalized Padé approximants, and the Villani limit theorem. The results depend only on the general structure of the partition function and certain monotonicity with system size properties which hold fairly generally.