This article is cited in 7 papers

Conditions for the nonuniqueness of the Gibbs state for lattice models having finite interaction potentials

V. M. Gercik


Abstract: 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.

UDC: 519.2

MSC: 82A40

Received: 22.10.1974

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:2, 429–443

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