Dynamics of domain walls in an incommensurate phase near the lock-in transition: One-dimensional crystal model

A phase transition from a high-symmetry to a low-symmetry commensurate phase through an incommensurate phase was studied in the framework of the one-dimensional elastically hinged molecule model which includes only a fourth-order anharmonic potential. The phase diagram with respect to the harmonic-potential coefficient and the external force was obtained. From the numerical analysis of the equation of motion, it was shown that the incommensurate phase near the lock-in transition contains a periodic system of energetically equivalent domain walls which are mutually repulsive. The properties of the domain walls were studied and the lock-in transition was described as the annihilation process of the walls when the repulsion is changed to attraction.