Abstract
On the basis of general inequalities in quantum statistical mechanics we derive a rigorous upper bound for the magnetization in the ferromagnetic quantum Heisenberg model with arbitrary spin and dimensionn≧3.
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Dyson, F. J., Lieb, E. H., Simon, B.: Phys. Rev. Lett.37, 120 (1976)
Roepstorff, G.: Commun. math. Phys.46, 253 (1976)
Naudts, J., Verbeure, A.: J. Math. Phys.17, 419 (1976)
Szabo, N.: On the phase transition inX Y- and Heisenberg models (preprint)
Ruelle, D.: Statistical mechanics. New York: Benjamin 1969
Mermin, N., Wagner, H.: Phys. Rev. Letters17, 1133 (1966)
Bloch, F.: Z. Physik61, 202 (1930)
Keffer, F.: Encyclopedia of physics, 18/2. Berlin-Heidelberg-New York: Springer 1966
Bochner, S.: Lectures on Fourier integrals. Princeton University Press 1959
Rudin, W.: Real and complex analysis. New York: McGraw Hill 1974
Loomis, L. H.: An introduction to abstract harmonic analysis. Princeton: Van Nostrand 1953
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Communicated by J. L. Lebowitz
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Roepstorff, G. A stronger version of Bogoliubov's inequality and the Heisenberg model. Commun.Math. Phys. 53, 143–150 (1977). https://doi.org/10.1007/BF01609128
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DOI: https://doi.org/10.1007/BF01609128