Nonconvex interactions: A mechanism for the occurrence of modulated order in condensed matter

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Abstract
We present a detailed analysis of one-dimensional models where frustration results from the presence of nonconvex interparticle interactions. The phase diagrams, obtained numerically, are qualitatively different depending on whether or not the particles, in the ground state, experience the nonconvex part of the interaction potential. When the particles experience only the convex part of the interaction potential, only phases where the winding number is uniquely defined are found and the transitions among these phases are suggestive of a complete devil’s-staircase behavior. When some of the particles, in the ground state, experience the nonconvex part of the interaction potential, phases where the winding number is not uniquely defined are found. In this case, both first- and second-order phase transitions and possibly quasicontinuous transitions are found. Also of interest is the existence of sequences of superdegenerate points where the system has residual entropy and violates the third law of thermodynamics. At these points, we show that the ground state consists of noninteracting solitons of zero energy.