Frenkel-Kontorova model with pinning cusps

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A Frenkel-Kontorova model with a piecewise concave parabolic potential with downward cusps such that atoms could be pinned at the potential minima is exactly solved. An infinite series of first-order transitions, which may be understood as the dissociation of a large "molecule" into two smaller ones, is found as the strength of the potential increases from zero. The minimum energy configurations need not have a well-defined winding number. Given the winding number, the ground state configurations in general are highly degenerate and it is shown that one of them can be depicted by an increasing hull function. A novel type of non-recurrent minimum energy configuration, which may be viewed as defects carrying "fractional charge", exists.

Original languageEnglish
Pages (from-to)30-42
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Issue number1
Publication statusPublished - 1997
Externally publishedYes


  • Area-preserving maps
  • Farey fraction
  • Fractional charge
  • Frenkel-Kontorova model
  • Harmless staircase

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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