Abstract
A model for incommensurate transitions proposed by Chen and Walker [Phys. Rev. B 43 (1991) 5634] has been extended to describe a sub-lattice model which possesses supersymmetry. If a zone boundary mode freezes, a superstructure with supersymmetry can appear and may transform into a superstructure without supersymmetry at lower temperature. Although both superstructures belong to the same space group, the transition is either second or first order one with accompanying a definite anomaly in specific heat and susceptibility.
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