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


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).


Neural Network Statistical Physic Complex System Stable State Nonlinear Dynamics 
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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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