Accurate determination of the translational correlation function of two-dimensional solids

• Main Authors: Li, Yan-Wei, Pica Ciamarra, Massimo
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Physics; Disclinations and Disclocations; Phase Transitions
• Online Access: https://hdl.handle.net/10356/138058
• Institution: Nanyang Technological University

The identification of the different phases of a two-dimensional (2D) system, which might be solid, hexatic, or liquid, requires the accurate determination of the correlation function of the translational and bond-orientational order parameters. According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, in the solid phase the translational correlation function decays algebraically, as a consequence of the Mermin-Wagner long-wavelength fluctuations. However, recent results have shown an exponential-like decay. By revisiting different definitions of the translational correlation function commonly used in the literature, here we clarify that the observed exponential-like decay in the solid phase results from an inaccurate determination of the symmetry axis of the solid; the expected power-law behavior is recovered when the symmetry axis is properly identified. We show that, contrary to the common assumption, the symmetry axis of a 2D solid is not fixed by the direction of its global bond-orientational parameter, and we introduce an approach allowing one to determine the symmetry axis from a real space analysis of the sample.