Geodesic
On the phase diagram in the Frenkel'--Kontorova model
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 3, pp. 459-464

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A probability measure invariant with respect to a two-dimensional transformation and describing the $T\to0$ limit of the Gibbs distribution in the Frenkel'–Kontorova model is investigated. The obtained result shows that for sufficiently high energies of the substrate the configurations of particles forming ground states are such that all particles are at points of minimum of the potential. 
@article{TMF_1983_57_3_a12,
     author = {A. Ya. Zaslavskii},
     title = {On the phase diagram in the {Frenkel'--Kontorova} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {459--464},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_57_3_a12/}
}
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A. Ya. Zaslavskii. On the phase diagram in the Frenkel'--Kontorova model. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 3, pp. 459-464. http://geodesic.mathdoc.fr/item/TMF_1983_57_3_a12/