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

TL;DR

This paper calculates the first-order interaction correction to the free energy of the quantum Heisenberg ferromagnet in the large spin limit, providing insights into the behavior of spin waves and their interactions.

Contribution

It introduces the first-order interaction correction to the free energy in the large-S limit, valid in 2D and 3D, and compares it with Dyson's low-temperature expansion.

Findings

First-order correction has expected temperature dependence.

Results valid for large spin S with fixed βS.

Highlights need for cancellations in higher-order corrections.

Abstract

The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculate the first order interaction correction to the free 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 is valid in two and three spatial dimensions. We extrapolate our result to compare with Dyson's low-temperature expansion. While our first-order correction has the expected temperature dependance, in higher orders of the perturbation theory cancellations are necessary.