Phase Transitions and Orientational Order in a Two Dimensional Lennard-Jones System
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It has long been suspected that the solid-fluid transition in two dimensions might be rather different than its 3-D counterpart, because of the lack of translational order in 2-D solids. Recently, a detailed theory of 2-D melting has been put forward by Halperin and Nelson.1 This theory provides a picture of 2-D melting that is indeed very different from what is observed in the three dimensional world. In particular, Halperin and Nelson (henceforth referred to as HN) make the intriguing prediction that, if 2-D melting is not a first order transition, then two second order transitions are required to go from the solid to the isotropic fluid phase. The solid and isotropic fluid phases will be separated by a peculiar liquid crystal-like phase which exhibits short range transiational order but long range “orientational” order.
KeywordsTriangular Lattice Orientational Order Melting Transition Orientational Order Parameter Isotropic Fluid
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