Ground-State Transition in a Two-Dimensional Frenkel–Kontorova Model

The ground state of a generalized Frenkel–Kontorova model with a transversal degree of freedom is studied. When the coupling strength, K, and the frequency of a single−atom vibration in the transversal direction, ω_0y, are increased, the ground state of the model undergoes a transition from a two−dimensional configuration to a one-dimensional one. This transition can manifest in different ways. Furthermore, we find that the prerequisite of a two-dimensional ground state is θ≠1/q.