Low-Temperature Spin-Wave Approximation for the Heisenberg Ferromagnet

We study the low temperature thermodynamics of the quantum Heisenberg ferromagnet in three dimension for any value of the spin $ S \geq 1/2 $. We report on a rigorous proof of the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy as the inverse temperature $ \beta \to \infty $.