Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel.
Proc Natl Acad Sci U S A. 2011 Jul 19;108(29):11804-9. doi: 10.1073/pnas.1014915108. Epub 2011 Jul 5.
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.
具有几何阻挫的材料具有基态简并性，这种简并性可能会被一些细微的效应消除，例如高阶相互作用会导致有序结构在能量上有微小的偏好。或者，有序可能是由无序序作用引起的构型之间的熵差异导致的。受最近在一个受挫胶体系统中实验的启发，该实验中推测有序是由熵引起的，我们在本文中考虑了在可变形三角形晶格上的反铁磁伊辛模型。我们在微观水平上精确地计算了位移，与之前的研究相反，我们发现了一种具有随机之字形条纹的部分无序基态。每个这样的构型都有不同的变形，因此具有独特的声子谱和不同的熵，在有限温度下消除了简并性。尽管如此，由于基态构型之间的自由能势垒，系统会落入无序的玻璃态。
