Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes

Abstract

We examine the shapes and energies of 5- and 7-fold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, $\kappa$, to the hexatic stiffness constant, $K_A$, suggesting {\em two} distinct Kosterlitz-Thouless defect proliferation temperatures. Seven-fold disclinations are studied in detail numerically for arbitrary $\kappa /K_A$. We argue that thermal fluctuations always drive $\kappa /K_A$ into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the {\em same} critical temperature. We show analytically that both types of defects have power law shapes with continuously variable exponents in the ``unbuckled'' regime. Thermal fluctuations then lock in specific power laws at long wavelengths, which we calculate for 5- and 7-fold defects at low temperatures.

LaTeX format. 17 pages. To appear in Phys. Rev. E

References in corpus (1)

• Topological Defects on Fluctuating Surfaces: General Properties and the Kosterlitz-Thouless Transition

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