| Abstract: | An important project, incommensurate phases and commensurate-incommensurate (CI)
transitions, in condensed matter physics is reviewed through the Frenkel-Kontorova(FK)
model. The reviews mainly focus on the one-dimensional case. We present the concepts,
physical pictures, mechanism, backgroud, objects and significance of the incommensurate
phases and CI transitions. Some basic theories and methods in the studies are given. We
briefly reviewed the advances of some special topics which include the standard FK model
and the generalized ones with convex interatomic interactions, the classical nonconvex FK
model, the quantum effects of the FK model, the FK model with one-dimensional diatomic
chain, the generalization of the FK modle to two-dimenisonal and three-dimensional cases,
the finite temperature effects of CI transitions. We also present some topics which need
more investigation. |
