Farey Tree and the Frenkel-Kontorova Model

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

We solved the Frenkel-Kontorova model with the potential $V(u)=-\frac{1}{2}|\lambda |(u-\mathrm{Int}[u]-\frac{1}{2}{)}^2$ exactly. For given $|\lambda |$, there exists a positive integer $q_c$ such…