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

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.

13 pages, 1 diagram; v2: extended introduction, references added

References in corpus (2)

• Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet
• The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

Cited by in corpus (6)

• Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime
• Correlation Energy of a Weakly Interacting Fermi Gas
• Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
• Bosonic Collective Excitations in Fermi Gases
• Bosonization of Fermionic Many-Body Dynamics
• Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation