Multiwell interparticle potentials are proposed as a mechanism for the occurrence of modulated phases. This is examined through two models with double-well interactions. For these systems, the effective potential method is reviewed and a certain process of calculation is emphasized. To characterize the modulated phases, the winding number omega, and the rotation number Omega are redefined. The method to recover the chain of particles and calculate the value of omega is given. We find that the phase diagrams strongly relate to the period of the external potential D. For each model, there is a threshold value in D, which equals to the distance between the two minimum value points. Within different interval of D, the phase diagrams exhibit different behavior. The periodicity of the phase diagram and the difference between modulated phases with the same Omega are also discussed.
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