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

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.

5 pages, 10 figures

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• Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY-spin model
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• Mean-field universality class induced by weak hyperbolic curvatures
• Critical Phenomena in Hyperbolic Space
• Avoided criticality and slow relaxation in frustrated two dimensional models
• Continuous Transition of Defect Configuration in a Deformed Liquid Crystal Film
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• Topological Phase Transitions in Superfluids Near Black Hole Horizons
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