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Kosterlitz-Thouless Transitions on Fluctuating Surfaces

Jeong-Man Park·T. C. Lubensky
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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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Jeong-Man Park, T. C. Lubensky. 1995-12-13. Kosterlitz-Thouless Transitions on Fluctuating Surfaces. https://arxiv.org/abs/cond-mat/9512107

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