### 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 |

### ASJC Scopus subject areas

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

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## Cite this

Kao, H. C., Lee, S. C., & Tzeng, W. J. (1997). Farey fractions and the Frenkel-Kontorova model.

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*55*(3), 2628-2631. https://doi.org/10.1103/PhysRevE.55.2628