Free energies of isolated five- and sevenfold disclinations in hexatic membranes

This is the authors' abstract. We don't add key points for this paper.

We examine the shapes and energies of five- and sevenfold disclinations in low-temperature hexatic membranes. These defects buckle at different values of the ratio of the bending rigidity, {κ}, to the hexatic stiffness constant, KA, suggesting two distinct Kosterlitz-Thouless defect proliferation temperatures. Sevenfold disclinations are studied in detail numerically for arbitrary {κ}/KA. We argue that thermal fluctuations always drive {κ}/KA into an ``unbuckled'' regime at long wavelengths, so that disclinations should, in fact, proliferate at the 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 five- and sevenfold defects at low temperatures. {} 1996 The American Physical Society.