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Journal of Statistical Physics

, Volume 26, Issue 4, pp 755–766 | Cite as

Energy gap, clustering, and the Goldstone theorem in statistical mechanics

  • L. Landau
  • J. Fernando Perez
  • W. F. Wreszinski
Articles

Abstract

We prove a Goldstone-type theorem for a wide class of lattice and continuum quantum systems, both for the ground state and at nonzero temperature. For the ground state (T=0) spontaneous breakdown of a continuous symmetry implies no energy gap. For nonzero temperature, spontaneous symmetry breakdown implies slow clustering (noL1 clustering). The methods apply also to nonzero-temperature classical systems.

Key words

Energy gap clustering Goldstone theorem 

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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • L. Landau
    • 1
  • J. Fernando Perez
    • 2
  • W. F. Wreszinski
    • 2
  1. 1.Mathematics Department, Bedford CollegeUniversity of LondonEngland
  2. 2.Instituto de FisicaUniversidade de São PauloBrazil

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