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, omega(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 theta not equal 1/q.