The ground state of the Frenkel–Kontorova model

Babushkin, A. Yu.; Abkaryan, A. K.; Dobronets, Boris S.; Krasikov, V. S.; Filonov, A. N.

doi:10.1134/s1063783416090080

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2021

2022

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Cited by 5 publications

(2 citation statements)

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“…It is clear that the result is not helpful for an original finite FK chain, see Figure 1. We note that many researchers have treated finite chains [9,33,35,54,[57][58][59][60][61][62][63][64][65] (to name a few); however, they use a useless contrast of rational with irrational numbers in the finite FK model.…”

Section: Discussionmentioning

confidence: 99%

An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model

Quapp

Bofill

2022

Electronics

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Section: Discussionmentioning

confidence: 99%

An Analysis of Some Properties and the Use of the Twist Map for the Finite Frenkel–Kontorova Model

Quapp

Bofill

2022

Electronics

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“…The cosine function specifies the periodic substrate potential. This simple approximation reveals a wide variety of ground states for the system [4][5][6] and different waves in the atoms chain [7][8][9]. Solitons are of the greatest interest.…”

Section: Introductionmentioning

confidence: 95%

Simulation of Epitaxial Film–Substrate Interaction Potential

2022

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The formation of the substrate surface potential based on the Lennard-Jones two-particle potential is investigated in this paper. A simple atom’s square lattice on the substrate surface is considered. The periodic potential of the substrate atoms is decomposed into a Fourier series. The amplitude ratio for different frequencies has been examined numerically. The substrate potential is approximated with high accuracy by the Frenkel–Kontorova potential at most parameter values. There is a field of parameters in which the term plays a significant role, with a period half as long as the period of the substrate atoms. The ground state of the monoatomic film is modeled on the substrate potential. The film may be in both crystalline and amorphous phases. The transition to the amorphous phase is associated with a change in the landscape of the substrate potential. There are introduced order parameters for structural phase transition in the thin film. When changing the parameters of the substrate, the order parameter experiences a jump when changing the phase of the film.

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