High-Temperature Series Expansions for the Spin-½ Heisenberg Model by the Method of Irreducible Representations of the Symmetric Group

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Abstract
We show how the partition functions for finite clusters with spin-½ Heisenberg interactions may be computed efficiently and generally to any desired number of powers in reciprocal temperature. As an example, we have expanded the zero-magnetic-field free energy to the twenty-first power for the linear Heisenberg model and for nonzero magnetic field give an expression good through the tenth power. We introduce the concept of the two-point Padé approximant and use it to analyze the energy for the linear Heisenberg model.