The ground state of the Frenkel–Kontorova model

The continual approximation of the ground state of the discrete Frenkel–Kontorova model is tested using a symmetric algorithm of numerical simulation. A “kaleidoscope effect” is found, which means that the curves representing the dependences of the relative extension of an $N$-atom chain vary periodically with increasing $N$. Stairs of structural transitions for $N\gg1$ are analyzed by the channel selection method with the approximation $N=\infty$. Images of commensurable and incommensurable structures are constructed. The commensurable–incommensurable phase transitions are stepwise.