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

References in corpus (6)

• Tuning the fragility of a glassforming liquid by curving space
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
• Hard Discs on the Hyperbolic Plane
• Critical properties of the three- and four-dimensional gauge glass
• Diffusion on a heptagonal lattice
• Phase diagram of generalized fully frustrated XY model in two dimensions

Cited by in corpus (1)

• Phase transition of $q$-state clock models on heptagonal lattices