Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

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

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 xy 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

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

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

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