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arXiv:1312.7873 · Communications in Mathematical Physics

Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet

Michele Correggi, Alessandro Giuliani, Robert Seiringer

Published Jun 22, 2015• 22 citations
arXivHTMLPDF
DOI
10.1007/s00220-015-2402-0

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Abstract. We consider the quantum ferromagnetic Heisenberg model in three di-mensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial con-tribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein–Primakoff representa-tion. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neighbor attraction. This attractive interaction makes the lower bound on the free energy particularly tricky: the key idea there is to prove a differential inequality for the two-particle density, which is thereby shown to be smaller than the probability density of a suitably weighted two-particle random process on the lattice. 1.