Stability properties and the KMS condition
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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).
KeywordsNeural Network Statistical Physic Complex System Stable State Nonlinear Dynamics
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