1996/08/27 by Jeong-Man Park, Park, Jeong-Man · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed Matter (cond-mat) #FOS: Physical sciences #Quantum, superfluid, helium dynamics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9608133
REVTEX, 22 pages with 3 postscript figures
arxiv created 1996/08/27 · openalex publication_date 1996/08/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the existence of the Kosterlitz-Thouless (KT) transition for n-atic tangent-plane order on a deformable spherical surface and investigate the development of quasi-long range n-atic order and the continuous shape changes below the KT transition in the low temperature limit. The n-atic order parameter ψ= exp[inΘ] describes, respectively, vector, nematic, and hexatic order for n=1,2, and 6. We derive a Coulomb gas Hamiltonian to describe it. We then convert it into the sine-Gordon Hamiltonian and find a linear coupling between a scalar field and the Gaussian curvature. After integrating over the shape fluctuations, we obtain the massive sine-Gordon Hamiltonian, where the interaction between vortices is screened. We find, for n2Kn/κ≪ 1/4, there is an effective KT transition. In the ordered phase, tangent-plane n-atic order expels the Gaussian curvature. In addition, the total vorticity of orientational order on a surface of genus zero is two. Thus, the ordered phase of an n-atic on such a surface will have 2n vortices of strength 1/n, 2n zeros in its order parameter, and a nonspherical equilibrium shape. Our calculations are based on a phenomenological model with a gauge-like coupling between ψ and curvature and close to the Abrikosov treatment of a type II superconductor.