Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 149, Issue 2, Pages 234-245Publisher
SPRINGER
DOI: 10.1007/s10955-012-0589-4
Keywords
Ferromagnetic Heisenberg model; Magnons; Spin waves
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Funding
- European Research Council under the European Union's Seventh Framework Programme ERC Starting Grant CoMBoS [239694]
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We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting bosons (magnons). We prove this fact at the level of the specific free energy: if S -> a and the inverse temperature beta -> 0 in such a way that beta S stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof is based on the localization of the system in small boxes and on upper and lower bounds on the local free energy, and it also provides explicit error bounds on the remainder.
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