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

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 kappa to the hexatic stiffness constant K-A suggesting two distinct Kosterlitz-Thouless defect proliferation temperatures. Sevenfold 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 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.