Abstract
Models of two-dimensional disordered materials, designed to illuminate the behavior of frustrated 2d liquids and solids, and provide insights into defect theories of the glass transition, are discussed. Important topological differences in the way particles pack in two, as opposed to three dimensions are emphasized. In d=2, one can introduce a controllable amount of disorder by varying the concentration of particles of the wrong size. Because of dislocation trapping by impurities, quenched analogues of the equilibrium hexatic phase appear at low temperatures. Large orientational correlation lengths characterize many nominally amorphous, translationally disordered particle configurations. Crystalline films with a quenched distribution of impurities become unstable at low temperatures, where thermally excited dislocation pairs are broken apart by the random impurity potential. Frustration can be introduced into arrays of identical particles by packing them on a manifold of constant negative curvature. The curvature can be chosen to mimic problems associated with dense random packing of tetrahedra in three dimensions. Some conjectures on the behavior of such arrays with decreasing temperature are presented.
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Nelson, D.R. (1983). Order, Frustration, and Two-Dimensional Glass. In: Yonezawa, F., Ninomiya, T. (eds) Topological Disorder in Condensed Matter. Springer Series in Solid-State Sciences, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82104-2_12
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DOI: https://doi.org/10.1007/978-3-642-82104-2_12
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