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 ofL 1-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, ofL 1-asymptotic abelian systems, by stability and cluster properties (a slight discrepancy can occur for infinite temperature states).
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Communicated by E. Lieb
Supported during this research by the Norwegian Research Council for Science and Humanities
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Bratteli, O., Kishimoto, A. & Robinson, D.W. Stability properties and the KMS condition. Commun.Math. Phys. 61, 209–238 (1978). https://doi.org/10.1007/BF01940765
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DOI: https://doi.org/10.1007/BF01940765