Deep Spin-Glass Hysteresis Area Collapse and Scaling in the $d=3$ $\pm J$ Ising Model

We investigate the dissipative loss in the $\pm J$ Ising spin glass in three dimensions through the scaling of the hysteresis area, for a maximum magnetic field that is equal to the saturation field. We perform a systematic analysis for the whole range of the bond randomness as a function of the sweep rate, by means of frustration-preserving hard-spin mean field theory. Data collapse within the entirety of the spin-glass phase driven adiabatically (i.e., infinitely-slow field variation) is found, revealing a power-law scaling of the hysteresis area as a function of the antiferromagnetic bond fraction and the temperature. Two dynamic regimes separated by a threshold frequency ${\omega }_c$ characterize the dependence on the sweep rate of the oscillating field. For $\omega <{\omega }_c$, the hysteresis area is equal to its value in the adiabatic limit $\omega =0$, while for $\omega >{\omega }_c$ it increases with the frequency through another randomness-dependent power law.