DIMERIZED GROUND-STATES OF THE FRENKEL-KONTOROVA MODEL WITH A TRANSVERSAL DEGREE-OF-FREEDOM

We consider the ground states of a generalized Frenkel-Kontorova model with a transversal degree of freedom. The substrate potential is taken to be sinusoidal in the longitudinal direction and parabolic in the transversal one. We assume that the atoms in the chain repel each other with a Coulomb law and that the interaction has a long-range scale. The trivial ground state in this system undergoes a phase transition to a dimerized (zigzag) ground state when the repulsion exceeds some critical value. We show that for much larger values of the interaction parameters there exists the next (zigzag-2) dimerized ground state which cannot be obtained from the previous one in a bifurcational way.