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.
DLR–KMS correspondence on lattice spin systems
Drago N.;
2023-01-01
Abstract
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.
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