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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
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Random Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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