Journal of Statistical Physics

, Volume 29, Issue 2, pp 159–175 | Cite as

The mermin-wagner phenomenon and cluster properties of one- and two-dimensional systems

  • C. A. Bonato
  • J. Fernando Perez
  • Abel Klein


We give optimal conditions concerning the range of interactions for the absence of spontaneous breakdown of continuous symmetries for one- and two-dimensional quantum and classical lattice and continuum systems. For a class of models verifying infrared bounds our conditions are necessary and sufficient. Using the same techniques we obtain “a priori” bounds on clustering for systems with continuous symmetry, improving results of Jasnow and Fisher.

Key words

Symmetry breaking cluster properties 


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Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • C. A. Bonato
    • 1
  • J. Fernando Perez
    • 1
  • Abel Klein
    • 2
  1. 1.Instituto de FisicaUniversidade de São PauloSão PauloBrazil
  2. 2.Department of MathematicsUniversity of CalforniaIrvine

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