Stability properties and the KMS condition |
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| Authors: | Ola Bratteli Akitaka Kishimoto Derek W Robinson |
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| Institution: | (1) Centre de Physique Théorique II, CNRS, F-13274 Marseille Cedex 2, France;(2) Département de Physique, Université d'Aix-Marseille II, Luminy, F-13274 Marseille;(3) Present address: Matematisk Institutt, Avd. A, Universitetet i Oslo, Blindern, Oslo 3, Norway;(4) Present address: Department of Mathematics, University of New South Wales, P.O. Box 1, 2033 Kensington, NSW, Australia |
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| 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).Supported during this research by the Norwegian Research Council for Science and Humanities |
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