Geodesic
Uniqueness of the limit Gibbs distribution in one-dimensional classical systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 1, pp. 100-108

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Uniqueness of the limit Gibbs distribution is proved for the one-dimensional latticesystems, in which the slow decreasing of the inter-particle interaction is allowed. The main restriction on the interaction potential $U(c)$ is $$ \sum_{c\colon0\in c,\,\operatorname{diam}\{c\}=K}\operatorname{diam}\{c\}|U(c)|\ln\ln K, $$ where $c=\{x_1,\dots,x_n\}$ is an arbitrary configuration of particles on the lattice and $B$ is some sufficiently small constant. 
@article{TMF_1975_24_1_a11,
     author = {R. A. Minlos and G. M. Natapov},
     title = {Uniqueness of the limit {Gibbs} distribution in one-dimensional classical systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {100--108},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_24_1_a11/}
}
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R. A. Minlos; G. M. Natapov. Uniqueness of the limit Gibbs distribution in one-dimensional classical systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 1, pp. 100-108. http://geodesic.mathdoc.fr/item/TMF_1975_24_1_a11/