Phys. Rev. B 37, 1898-1912 (1988)

                                          [Issue 4 - February 1988 ]

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

     Mario Marchand, Kevin Hood, and Alain Caillé 
     Département de Physique et Centre de Recherche en Physique du Solide,
Université de Sherbrooke, Sherbrooke, Québec,
     Canada J1K||2R1

Received 14 August 1987

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.

©1988 The American Physical Society

URL: http://publish.aps.org/abstract/PRB/v37/p1898
PACS: 64.60.-i, 05.70.Fh