Communications in Mathematical Physics

, Volume 42, Issue 1, pp 31–40 | Cite as

Absence of breakdown of continuous symmetry in two-dimensional models of statistical physics

  • R. L. Dobrushin
  • S. B. Shlosman


Two-dimensional lattice model is considered. The connected Lie groupG acts on a configuration space. The Gibbs potential assumed to be invariant under this action. We prove, that under general assumption on the potential, each Gibbs random field with this potential is alsoG-invariant.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Random Field 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • R. L. Dobrushin
    • 1
  • S. B. Shlosman
    • 1
  1. 1.Institute for Problems of Information-TransmissionMoscowUSSR

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