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

We examine the shapes and energies of 5and 7-fold 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. Seven-fold 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 5and 7-fold defects at low temperatures. PACS 05.70.Jk, 68.10.-m, 87.22.Bt