Low-Temperature Spin-Wave Approximation for the Heisenberg Ferromagnet

TL;DR

This paper rigorously proves that the spin-wave approximation accurately describes the low-temperature thermodynamics of the three-dimensional quantum Heisenberg ferromagnet for all spins $S \\geq 1/2$, especially regarding the free energy.

Contribution

It provides a rigorous validation of the spin-wave approximation for the excitation spectrum at low temperatures in the 3D quantum Heisenberg ferromagnet.

Findings

Validation of spin-wave approximation for free energy at low temperatures

First non-trivial contribution to the free energy confirmed

Applicable for all spins $S \\geq 1/2$ in 3D

Abstract

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 $.