Kosterlitz-Thouless Transitions on Fluctuating Surfaces

1995/12/13 by Jeong-Man Park, Park, Jeong-Man, T. C. Lubensky +1
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/9512107

REVTEX, 11 pages with 2 postscript figures compressed using uufiles

arxiv created 1995/12/13 · openalex publication_date 1995/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the Kosterlitz-Thouless transition for hexatic order on a free fluctuating membrane and derive both a Coulomb gas and a sine-Gordon Hamiltonian to describe it. In the former, both disclinations and Gaussian curvature contribute to the charge density. In the latter, there is a linear coupling between a scalar field and the Gaussian curvature. We derive renormalization group recursion relations that predict a transition with decreasing bending rigidity κ. Using the sine-Gordon model, we show that there is no KT transition on a deformable sphere.

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