### Abstract

We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2[formula presented]/2 exactly. For given λ>0, there exists a positive integer [formula presented] such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the [formula presented]th row of Farey fractions. For fixed ω=p/q, there is a critical [formula presented] when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey fractions.

Original language | English |
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Pages (from-to) | 2628-2631 |

Number of pages | 4 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 55 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1997 Jan 1 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*55*(3), 2628-2631. https://doi.org/10.1103/PhysRevE.55.2628

**Farey fractions and the Frenkel-Kontorova model.** / Kao, Hsien-Chung; Lee, Shih Chang; Tzeng, Wen Jer.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 55, no. 3, pp. 2628-2631. https://doi.org/10.1103/PhysRevE.55.2628

}

TY - JOUR

T1 - Farey fractions and the Frenkel-Kontorova model

AU - Kao, Hsien-Chung

AU - Lee, Shih Chang

AU - Tzeng, Wen Jer

PY - 1997/1/1

Y1 - 1997/1/1

N2 - We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2[formula presented]/2 exactly. For given λ>0, there exists a positive integer [formula presented] such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the [formula presented]th row of Farey fractions. For fixed ω=p/q, there is a critical [formula presented] when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey fractions.

AB - We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2[formula presented]/2 exactly. For given λ>0, there exists a positive integer [formula presented] such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the [formula presented]th row of Farey fractions. For fixed ω=p/q, there is a critical [formula presented] when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey fractions.

UR - http://www.scopus.com/inward/record.url?scp=0642316182&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0642316182&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.55.2628

DO - 10.1103/PhysRevE.55.2628

M3 - Article

VL - 55

SP - 2628

EP - 2631

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 3

ER -