The ground state of the Frenkel–Kontorova model

Abstract

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 ≫ 1 are analyzed by the channel selection method with the approximation N = ∞. Images of commensurable and incommensurable structures are constructed. The commensurable–incommensurable phase transitions are stepwise.