Some developments in the theory of modulated order. II. Deformable-lattice models and the axial next-nearest-neighbor Ising model as a random magnet

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Abstract
This paper presents a new class of models capable of producing modulated order with solely nearest-neighbor forces. These deformable-lattice models create modulated phases out of the interaction between spin and elastic degrees of freedom through a polarization, or feedback, mechanism—as opposed to the purely spin or purely elastic models that employ either competing force or competing periodicity mechanisms. We show that one of the deformable-lattice models, in particular, can be formally reduced to the axial-next-nearest-neighbor Ising (ANNNI) model. This observation turns out to imply, first, that the ANNNI model can be regarded as an ordinary Ising model with a distribution of coupling constants (a random magnet), and second, that other spin models might be profitably thought of not as Hamiltonians, but as potentials of mean force resulting from integrating out elastic degrees of freedom. The possible implications are considered for both the range and nature of the interaction between chemisorbed species as well as that between intercalates in graphite.