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The ground state of the Frenkel–Kontorova model

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Abstract

The continual approximation of the ground state of the discrete Frenkel–Kontorova model is tested using a symmetric algorithm of numerical simulation. A “kaleidoscope effect” is found, which means that the curves representing the dependences of the relative extension of an N-atom chain vary periodically with increasing N. Stairs of structural transitions for N ≫ 1 are analyzed by the channel selection method with the approximation N = ∞. Images of commensurable and incommensurable structures are constructed. The commensurable–incommensurable phase transitions are stepwise.

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Authors and Affiliations

  1. Institute of Space and Informatic Technologies, Siberian Federal University, ul. Kirenskogo 26, Krasnoyarsk, 660074, Russia

    A. Yu. Babushkin, A. K. Abkaryan, B. S. Dobronets & V. S. Krasikov

  2. Institute of Nonferrous Metals and Material Science, Siberian Federal University, pr. im. Gazety Krasnoyarskii Rabochii 95, Krasnoyarsk, 660025, Russia

    A. N. Filonov

Authors
  1. A. Yu. Babushkin
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  2. A. K. Abkaryan
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  3. B. S. Dobronets
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  4. V. S. Krasikov
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  5. A. N. Filonov
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Correspondence to A. Yu. Babushkin.

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Original Russian Text © A.Yu. Babushkin, A.K. Abkaryan, B.S. Dobronets, V.S. Krasikov, A.N. Filonov, 2016, published in Fizika Tverdogo Tela, 2016, Vol. 58, No. 9, pp. 1772–1782.

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Babushkin, A.Y., Abkaryan, A.K., Dobronets, B.S. et al. The ground state of the Frenkel–Kontorova model. Phys. Solid State 58, 1834–1845 (2016). https://doi.org/10.1134/S1063783416090080

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  • DOI: https://doi.org/10.1134/S1063783416090080

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