Order by disorder in the antiferromagnetic Ising model on an elastic triangular lattice

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Abstract

Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher-order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order by disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level and, contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state.

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Shokef, Y., Souslov, A., & Lubensky, T. C. (2011). Order by disorder in the antiferromagnetic Ising model on an elastic triangular lattice. Proceedings of the National Academy of Sciences of the United States of America, 108(29), 11804–11809. https://doi.org/10.1073/pnas.1014915108

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