Fractal spin glass properties of low energy configurations in the Frenkel-Kontorova chain

We study, numerically and analytically, the classical one-dimensional Frenkel-Kontorova chain in the regime of pinned phase characterized by phonon gap. Our results show the existence of exponentially many static equilibrium configurations that are exponentially close to the energy of the ground state. The energies of these configurations form a fractal quasidegenerate band structure that is described on the basis of elementary excitations. Contrary to the ground state, the configurations inside these bands are disordered.