Abstract
When the ordinary nearest-neighbor -state clock model (discrete model) is generalized to include asymmetric interactions, an incommensurate phase appears for integer in addition to the usual liquid and commensurate phases. Aside from being theoretically interesting, it is of practical importance in studies of the commensurate-incommensurate transition where the existence of a discrete nearest-neighbor model with this property gives a computational advantage over further-neighbor and continuum models. For , the incommensurate phase always has a high degree of discommensuration and a Lifshitz point will occur where the incommensurate, liquid, and commensurate phases coincide. For no incommensurate phase occurs. The system is analyzed at low temperature using a transfer matrix technique recently used by J. Villain and P. Bak to analyze a similar model with further-neighbor interactions.
- Received 15 December 1980
DOI:https://doi.org/10.1103/PhysRevB.24.398
©1981 American Physical Society