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arXiv · 0811.1895

Curvature-induced frustration in the $XY$ model on hyperbolic surfaces

Seung Ki Baek·Hiroyuki Shima·Beom Jun Kim
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Abstract

We study low-temperature properties of the $XY$ spin model on a negatively curved surface. Geometric curvature of the surface gives rise to frustration in local spin configuration, which results in the formation of high-energy spin clusters scattered over the system. Asymptotic behavior of the spin-glass susceptibility suggests a zero-temperature glass transition, which is attributed to multiple optimal configurations of spin clusters due to nonzero surface curvature of the system. It implies that a constant ferromagnetic spin interaction on a regular lattice can exhibit glasslike behavior without possessing any disorder if the lattice is put on top of a negatively curved space such as a hyperbolic surface.

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Seung Ki Baek, Hiroyuki Shima, Beom Jun Kim. 2009-07-17. Curvature-induced frustration in the $XY$ model on hyperbolic surfaces. https://doi.org/10.1103/physreve.79.060106

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