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

Yair Shokef*, Anton Souslov, T. C. Lubensky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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.

Original languageEnglish
Pages (from-to)11804-11809
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number29
StatePublished - 19 Jul 2011
Externally publishedYes


FundersFunder number
National Science Foundation
Directorate for Mathematical and Physical Sciences0520020


    • Colloidal monolayer
    • Geometric frustration
    • Magnetoelasticity


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