Spin-s spin-glass phases in the d=3 Ising model

All higher-spin (s≥1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3, exactly on a d=3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s→∞. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of λ=1.93 and runaway exponent of y_{R}=0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at p_{t}=0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.