Phase diagrams of one-dimensional commensurate-incommensurate transition model with triple-well interactions

We generalize the Frenkel-Kontorov model to the Frenkel-Kontorova-Devonshir e model in which the interaction is the triple-well potential. By use of th e 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 omega a nd the rotation number Omega, we analyze the periodicity of the phase diagr am and find some complex but regular phase structures. The properties of th e phase structures are closely related to the period of the external potent ial D.