Symmetry-breaking commensurate states in generalised Frenkel-Kontorova models

Ground states of classical, one-dimensional systems consisting of atoms connected with harmonic springs subject to a periodic, symmetric potential are studied. It is shown that some choices of the periodic potential yield periodic (commensurate) ground states lacking the reflection symmetry of the Hamiltonian. The phase diagram of the ground states of a specific model which exhibits asymmetric commensurate phases is studied in detail. The transition from an asymmetric commensurate state to an incommensurate state is mediated by two types of solitons (discommensurations), while that from a symmetric one is mediated by a single type of soliton. Solitons are symmetric or asymmetric depending on the model parameters. First- and second-order transitions between symmetric and asymmetric states with the same period occur as the strength of the potential is varied. The soliton that mediates transitions from a commensurate to an incommensurate state changes its character infinitely many times as a first-order transition line is approached.