Farey fractions and the Frenkel-Kontorova model

Hsien-Chung Kao, Shih Chang Lee, Wen Jer Tzeng

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)2628-2631
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume55
Issue number3
DOIs
Publication statusPublished - 1997 Jan 1

Fingerprint

Farey Fractions
Frenkel-Kontorova Model
Phase Transition
Winding number
First-order Phase Transition
integers
enthalpy
Molecules
dissociation
Integer
molecules

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 55, No. 3, 01.01.1997, p. 2628-2631.

Research output: Contribution to journalArticle

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