Phase Diagrams of One-Dimensional Commensurate-Incommensurate Transition Model with Triple-Well Interactions

We generalize the Frenkel-Kontorov model to the Frenkel-Kontorova-Devonshire model in which the interaction is the triple-well potential. By use of the effective potential method, numerical solutions of eigenvalue problem are used to work out the exact phase diagrams of a triple-well potential W and a piecewise parabolic potential V. According to the winding number ω and the rotation number Ω, we analyze the periodicity of the phase diagram and find some complex but regular phase structures. The properties of the phase structures are closely related to the period of the external potential D.