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 bounds can be established from the early power series coefficients for a wider class of functions than was previously possible. These procedures are proved to be applicable to many thermodynamic properties of the ferromagnetic Ising model and used thereon. Although nonbounding calculational procedures are shown to be satisfactory for most states of the system, certain pitfalls of those procedures are noted near the critical points.