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

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

2008-11-12

arxiv.org/abs/0811.1895v2

Phys. Rev. E 79, 060106(R) (2009)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 10 figures

Scientific paper

10.1103/PhysRevE.79.060106

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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