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Communications in Mathematical Physics

, Volume 61, Issue 3, pp 209–238 | Cite as

Stability properties and the KMS condition

  • Ola Bratteli
  • Akitaka Kishimoto
  • Derek W. Robinson
Article

Abstract

First we derive stability properties of KMS states and subsequently we derive the KMS condition from stability properties. New results include a convergent perturbation expansion for perturbed KMS states in terms of appropriate truncated functions and stability properties of ground states. Finally we extend the results of Haag, Kastler, Trych-Pohlmeyer by proving that stable states ofL1-asymptotically abelian systems which satisfy a weak three point cluster property are automatically KMS states. This last theorem gives an almost complete characterization of KMS states, ofL1-asymptotic abelian systems, by stability and cluster properties (a slight discrepancy can occur for infinite temperature states).

Keywords

Neural Network Statistical Physic Complex System Stable State Nonlinear Dynamics 
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 1978

Authors and Affiliations

  • Ola Bratteli
    • 1
  • Akitaka Kishimoto
    • 1
  • Derek W. Robinson
    • 1
    • 2
  1. 1.Centre de Physique Théorique II, CNRSMarseille Cedex 2France
  2. 2.Département de PhysiqueUniversité d'Aix-Marseille II, LuminyMarseille

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