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Journal of Statistical Physics

, Volume 18, Issue 4, pp 335–383 | Cite as

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

  • Freeman J. Dyson
  • Elliott H. Lieb
  • Barry Simon
Articles

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.

Key words

Phase transitions Heisenberg ferromagnet 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Freeman J. Dyson
    • 1
  • Elliott H. Lieb
    • 2
  • Barry Simon
    • 2
  1. 1.Institute for Advanced StudyPrinceton
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonNew Jersey

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