Deep spin-glass hysteresis-area collapse and scaling in the three-dimensional ±J Ising model

Abstract

We investigate the dissipative loss in the ±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 ω[subscript c] characterize the dependence on the sweep rate of the oscillating field. For ω<ω[subscript c], the hysteresis area is equal to its value in the adiabatic limit ω=0, while for ω>ω[subscript c] it increases with the frequency through another randomness-dependent power law.