Convergent, Bounding Approximation Procedures with Applications to the Ferromagnetic Ising Model

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Abstract
The Padé-approximant method is generalized in such a way that converging upper and lower bonds can be established from the early power-series coefficients for a wider class of functions than was previously possible. These procedures are proved applicable to many thermodynamic properties of the ferromagnetic Ising model and used thereon. Certain pitfalls of nonbounding calculational methods, when applied to this problem, are noted.