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 take n to be sinusoidal in the longitudinal direction and parabolic in the transversal one. We assume that the atoms in the chain repel each othe r with a Coulomb law and that the interaction has a long-range scale. The trivial ground state in this system undergoes a phase transition t o a dimerized (zigzag) ground state when the repulsion exceeds some cr itical value. We show that for much larger values of the interaction p arameters there exists the next (zigzag-2) dimerized ground state whic h cannot be obtained from the previous one in a bifurcational way.