Frustration in vicinity of transition point of Ising spin glasses

Abstract

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.

7 pages, 5 figures, version 2: higher-dimensional cases are mentioned in summary and discussion

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• Locations of multicritical points for spin glasses on regular lattices
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Cited by in corpus (5)

• Computational hardness of spin-glass problems with tile-planted solutions
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• An extension of estimation of critical points in ground state for random spin systems
• A simple relation between frustration and transition points in diluted spin glasses
• Analytical estimates of the locations of phase transition points in the ground state for the bimodal Ising spin glass model in two dimensions