Geodesic
Conditions for the nonuniqueness of the Gibbs state for lattice models having
Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 429-443

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The nonuniqueness of the Gibbs state is demonstrated for discrete lattice models having finite periodic interaction potentials which obey the so-called Peierls' condition. The limit points of the set of Gibbs states correspond to the periodic ground states for the models, which compose an orbit relative to the group of transformations leaving the potential invariant. The proof is based on a deduction of Peierls' estimates for the corresponding outer boundaries. Bibliography: 16 titles. 
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     author = {V. M. Gercik},
     title = {Conditions for the nonuniqueness of the {Gibbs} state for lattice models having},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a11/}
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V. M. Gercik. Conditions for the nonuniqueness of the Gibbs state for lattice models having. Izvestiya. Mathematics , Tome 10 (1976) no. 2, pp. 429-443. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a11/