1304.5722 (Ryoji Miyazaki)

Frustration in the vicinity of transition point of the Ising spin
glasses    [PDF]

Ryoji Miyazaki

We conjecture the existence of a relationship between frustration and the transition point at zero temperature of the 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 the Ising spin glasses with binary couplings on the two-dimensional lattices, the hierarchical lattices, and the three-body Ising spin glasses with binary couplings on the 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.

View original: http://arxiv.org/abs/1304.5722