2008/11/30 by Seung Ki Baek, Hiroyuki Shima, Beom Jun Kim · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.79.060106
published as Phys. Rev. E 79, 060106(R) (2009) · 5 pages, 10 figures
openalex publication_date 2009/06/22 · arxiv created 2009/07/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.