DLR–KMS correspondence on lattice spin systems

The Dobrushin–Lanford–Ruelle condition (Dobrushin in Theory Prob Appl 17:582–600, 1970. https://doi.org/10.1137/1115049 ; Lanford and Ruelle in Commun Math Phys 13:194–215, 1969. https://doi.org/10.1007/BF01645487 ) and the classical Kubo–Martin–Schwinger (KMS) condition (Gallavotti and Verboven in...

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Bibliographic Details
Published in:Letters in mathematical physics 2023-07, Vol.113 (4), Article 88
Main Authors: Drago, N., van de Ven, C. J. F.
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:The Dobrushin–Lanford–Ruelle condition (Dobrushin in Theory Prob Appl 17:582–600, 1970. https://doi.org/10.1137/1115049 ; Lanford and Ruelle in Commun Math Phys 13:194–215, 1969. https://doi.org/10.1007/BF01645487 ) and the classical Kubo–Martin–Schwinger (KMS) condition (Gallavotti and Verboven in Nuov Cim B 28:274–286, 1975. https://doi.org/10.1007/BF02722820 ) are considered in the context of classical lattice systems. In particular, we prove that these conditions are equivalent for the case of a lattice spin system with values in a compact symplectic manifold by showing that infinite-volume Gibbs states are in bijection with KMS states.
ISSN:1573-0530
1573-0530
DOI:10.1007/s11005-023-01710-x