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Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

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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 1/2x-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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Authors and Affiliations

  1. Institute for Advanced Study, Princeton, New Jersey

    Freeman J. Dyson

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

    Elliott H. Lieb & Barry Simon

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

Research supported by U.S. National Science Foundation under grants GP-40768X (F.J.D.), MCS 75-21684 (E.H.L.), and GP-39048 (B.S.).

Alfred Sloan Fellow.

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Dyson, F.J., Lieb, E.H. & Simon, B. Phase transitions in quantum spin systems with isotropic and nonisotropic interactions. J Stat Phys 18, 335–383 (1978). https://doi.org/10.1007/BF01106729

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  • DOI: https://doi.org/10.1007/BF01106729

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