Discrete lattice effects in incommensurate systems

The behaviour of systems which exhibit both commensurate and incommensurate phases is studied for a discrete lattice model. Close to the lock-in transition the incommensurate phase is shown to be well described by a soliton theory in which the solitons may be pinned to the lattice. This pinning effect leads to a 'devil's staircase' type of behaviour and causes an energy gap in the phason spectrum. It is also shown that an entropy-driven unpinning transition may take place dividing the incommensurate phase into a region in which the soliton density changes discontinuously and the phase is not strictly incommensurate, and a region in which the soliton density changes continuously and the phase is strictly commensurate.