Journal of Statistical Physics

, Volume 26, Issue 3, pp 505–512 | Cite as

On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions

  • Abel Klein
  • Lawrence J. Landau
  • David S. Shucker


Using the Bogoliubov inequality, we extend previously known results concerning the absence of continuous symmetry breakdown for equilibrium states of certain quantum and classical lattice, and continuum systems in two space dimensions.

Key words

Bogoliubov inequality symmetry breaking 


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  1. 1.
    N. D. Mermin and H. Wagner,Phys. Rev. Lett. 17:1133–1136 (1966).Google Scholar
  2. 2.
    N. D. Mermin,J. Math. Phys. 8:1061–1064 (1967).Google Scholar
  3. 3.
    I. C. Garrison, H. L. Morrison, and I. Wong,J. Math. Phys. 13:1735–1742 (1972).Google Scholar
  4. 4.
    R. L. Dobrushin and S. B. Shlosman,Commun. Math. Phys. 42:31–40 (1975).Google Scholar
  5. 5.
    J. Bricmont, J. Lebowitz, and C. Pfister,J. Stat. Phys. 21:573–582 (1979).Google Scholar
  6. 6.
    H. Araki,Commun. Math. Phys. 44:1–7 (1975).Google Scholar
  7. 7.
    H. Kunz and C. E. Pfister,Commun. Math. Phys. 46:245–251 (1976).Google Scholar
  8. 8.
    J. Fröhlich, R. Israel, E. Lieb, and B. Simon,Commun. Math. Phys. 62:1–34 (1978).Google Scholar
  9. 9.
    S. B. Shlosman,Commun. Math. Phys. 71:207–212 (1980).Google Scholar
  10. 10.
    W. Driessler, L. Landau, and J. F. Perez,J. Stat. Phys. 20:123–162 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Abel Klein
    • 1
  • Lawrence J. Landau
    • 2
  • David S. Shucker
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA
  2. 2.Mathematics Department, Bedford CollegeUniversity of LondonLondonEngland
  3. 3.Department of MathematicsUniversity of CaliforniaIrvineUSA

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