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

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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 ß S is fixed (ß 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 dependence, in higher orders of the perturbation theory cancellations are necessary.

Keywords

Ferromagnetic Heisenberg model Quantum Heisenberg Ferromagnet Magnon Spin-wave theory Interaction correction Holstein-Primakoff transformation Holstein-Primakov transformation Perturbation theory of the Heisenberg model 

Mathematics Subject Classification (2010)

82D40 82B10 82B20 81T28 81T25 
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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.QMATH, Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

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