2013/04/30 by Ryoji Miyazaki · 5 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Antiferromagnetism #Complex Systems and Time Series Analysis #Condensed matter physics #Critical point (mathematics) #Ferromagnetism #Frustration #Ising model #Mathematics #Physics #Spin (aerodynamics) #Spin glass #Theoretical and Computational Physics #Thermodynamics #Topological and Geometric Data Analysis #Transition point #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.7566/jpsj.82.094001
published in Journal of the Physical Society of Japan 82(9), 094001 (Physical Society of Japan) · 7 pages, 5 figures, version 2: higher-dimensional cases are mentioned in summary and discussion
arxiv created 2013/08/02 · openalex publication_date 2013/08/02 · arxiv updated 2013/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is close to the critical concentration at zero temperature when the output of a function about frustration is equal to unity. The function is the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds. This relation is conjectured in Ising spin glasses with binary couplings on two-dimensional lattices, hierarchical lattices, and three-body Ising spin glasses with binary couplings on two-dimensional lattices. In addition, the same argument in the Sherrington-Kirkpatrick model yields a point that is identical to the replica-symmetric solution of the transition point at zero temperature.