Padé Approximant Bounds for the Magnetic Susceptibility in the Three-Dimensional, Spin-½ Heisenberg Model

Abstract

We show that the analytical properties of a function and the first few terms of its power series may be utilized to obtain upper and lower bounds for a function and its derivative. We apply this technique to the Heisenberg-model susceptibility series and show that they diverge like ${(1-\frac{T}{T_c})}^{-\gamma }$ at the Curie point, where $\gamma$ is very closely $\frac{4}{3}$. Fairly accurate values of the Curie point are given for three lattices.