Title

The Geometrical Structure of 2d Bond-Orientational Order

Author(s)/Creator(s)

Mark Bowick, Department of Physics, Syracuse University, Syracuse, NYFollow
Alex Travesset, Syracuse University

Document Type

Article

Date

3-14-2001

Language

English

Disciplines

Physics

Description/Abstract

We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the intrinsic frustration for two-dimensional crystals with arbitrary geometry. Within a Debye-Huckel approximation, torsion may be identified as the density of dislocations. Changes in the geometry of the system cause a reorganization of the torsion density that preserves bond-orientational order. As a byproduct, we are able to derive several identities involving the topology, defect density and geometric invariants such as Gaussian curvature. The formalism is used to derive the general free energy for a 2D sample of arbitrary geometry, both in the crystalline and hexatic phases. Applications to conical and spherical geometries are briefly addressed.

Additional Information

22 pages, LaTeX, 4 eps figures Published version More information at http://arxiv.org/abs/cond-mat/0005356

Recommended Citation

Bowick, Mark and Travesset, Alex, "The Geometrical Structure of 2d Bond-Orientational Order" (2001). Physics - All Scholarship. 160.
https://surface.syr.edu/phy/160

Source

Harvested from Arxiv.org

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.