Farey fractions and the Frenkel-Kontorova model

Hsien chung Kao, Shih Chang Lee, Wen Jer Tzeng

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)2628-2631
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number3
Publication statusPublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'Farey fractions and the Frenkel-Kontorova model'. Together they form a unique fingerprint.

Cite this