Phase diagrams of two FKD models with different triple-well interactions

We introduce two typical Frenkel-Kontorova-Devonshire (FKD) models where th e interactions are of different triple-well potentials and the external pot entials are of the same parabolic type. The exact phase diagrams are worked out by the use of the effective potential method with the numerical implem entation. We also analyze the periodicity of the phase diagrams and find th at the propel-ties of the phase structures are closely related to the perio d of the external potential D.