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Free Energies of Isolated 5- and 7-fold Disclinations in Hexatic Membranes | | Michael W. Deem
; David R. Nelson
; | | Date: |
11 Dec 1995 | | Subject: | cond-mat | | Affiliation: | Harvard University), David R. Nelson (Harvard University | | 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. | | Source: | arXiv, cond-mat/9512079 | | Services: | Forum | Review | PDF | Favorites | |
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