Anharmonic effects in a finite Frenkel–Kontorova type chain

The features of the ground state and the phonon frequency spectrum of a finite Frenkel–Kontorova type model are investigated in presence of quartic anharmonic nearest-neighbor interactions. The different computational techniques used allow us to determine with great accuracy the critical parameter for the ground-state symmetry breaking transition, showing its dependence on the strength of the interatomic anharmonicity introduced. The phonon gap, the linearized vibrational modes and their parity are also studied in the vicinity of the transition point.