Various phase transitions in models for coupled charge-density waves are investigated by means of the $\epsilon$ expansion, mean-field theory, and Monte Carlo simulations. At zero temperature the effective action for the system with appropriate commensurability effects is mapped onto the three- or four-dimensional $\mathrm{XY}$ model, depending on spatiotemporal fluctuations, under the corresponding symmetry-breaking fields. It is revealed that the three- and four-dimensional systems display a single transition between the clock order (with broken $Z_M$ symmetry) and disorder. The nature of the phase transition depends crucially on the commensurability factor M: For $M>~4,$ in particular, the transition belongs to the same university class as the $\mathrm{XY}$ model. On the other hand, in the presence of misfit causing frustration in the charge-density wave, the interchain coupling is observed to favor either the commensurate state or the incommensurate state depending on the initial configuration; this gives rise to hysteresis around the commensurate-incommensurate transition. Boundaries separating such phases with different symmetries are obtained in the parameter space consisting of the temperature, symmetry-breaking field, fluctuation strength, interchain coupling, and misfit.

• Received 16 October 2003

DOI:https://doi.org/10.1103/PhysRevB.69.115117