2013 Volume 19 Issue 1 Pages 43-49
A relationship between frustration and the transition point at zero temperature of the Ising spin glasses is reported. We find that the concentration of antiferromagnetic bonds in the system is in good agreement with the critical concentration at zero temperature when the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds is equal to unity. This relation is confirmed 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. 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.
