Abstract
A method for the theoretical description of incommensurable phases is presented and a single-parameter symmetry group of these phases is found. A representation for the free energy of the aperiodic configurations is found. Existence conditions for a solution that extremalizes the specific free energy are found, and a small branch theorem is proved. A global solution is found in terms of elementary functions for an extremal configuration. The existence of a phase transition from an incommensurable phase into other phases as a function of exchange interactions is proved.
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