Previous studies of a charge-density-wave (CDW) model (originally proposed by McMillan) showed that near the lock-in transition the most stable CDW state has a series of equally spaced discommensurations—regions of localized rapid variation of the phase representing a superposition of sine-Gordon-type solitons. If the CDW system is sufficiently close to the lock-in (incommensurate to commensurate) transition such that the identity of the discommensurations are reasonably well defined, the system can be considered to be a lattice of particles free to vibrate about their equilibrium positions due to thermal fluctuations. We present a model for a three-dimensional lattice of discommensurations and calculate the corrections to the harmonics of the order parameter due to thermal fluctuations. We find that even though the mean-square displacement diverges at lock-in, the correction to the harmonics vanishes in that limit. We also calculate the phonon contribution to the free energy and find that the transition remains continuous.

• Received 13 March 1978

DOI:https://doi.org/10.1103/PhysRevB.18.2500