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Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

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Statistical Mechanics

Abstract

We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2 x−y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.

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Author information

Authors and Affiliations

  1. Institute for Advanced Study, Princeton, New Jersey, USA

    Freeman J. Dyson

  2. Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey, USA

    Elliott H. Lieb & Barry Simon (Alfred Sloan Fellow)

Authors
  1. Freeman J. Dyson
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  2. Elliott H. Lieb
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  3. Barry Simon
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, One Shields Ave., 95616-8633, Davis, CA, USA

    Bruno Nachtergaele

  2. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Jan Philip Solovej

  3. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090, Wien, Austria

    Jakob Yngvason

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© 1978 Springer-Verlag Berlin Heidelberg

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Dyson, F.J., Lieb, E.H., Simon, B. (1978). Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_12

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  • DOI: https://doi.org/10.1007/978-3-662-10018-9_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-06092-2

  • Online ISBN: 978-3-662-10018-9

  • eBook Packages: Springer Book Archive

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