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 ae << 1 are analyzed by the channel selection method with the approximation N = a. Images of commensurable and incommensurable structures are constructed. The commensurable-incommensurable phase transitions are stepwise.