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The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms ofinteracting bosons (called spin waves or magnons) as an expansion in theinverse spin size. We calculate the first order interaction correction to thefree energy, as an upper bound in the limit where the spin size $S \to \infty$and $\beta S$ is fixed ($\beta$ being the inverse temperature). Our result isvalid in two and three spatial dimensions. We extrapolate our result to comparewith Dyson's low-temperature expansion. While our first-order correction hasthe expected temperature dependance, in higher orders of the perturbationtheory cancellations are necessary.

Interaction Corrections to Spin-Wave Theory in the Large-S Limit of the Quantum Heisenberg Ferromagnet