Field-driven hysteresis of the d=3 Ising spin glass: Hard-spin mean-field theory

Hysteresis loops are obtained in the Ising spin-glass phase in d=3 using frustration-conserving hard-spin mean-field theory. The system is driven by a time-dependent random magnetic field H_Q that is conjugate to the spin-glass order Q, yielding a field-driven first-order phase transition through the spin-glass phase. The hysteresis loop area A of the Q−H_Q curve scales with respect to the sweep rate h of magnetic field as A−A₀∼h^b. In the spin-glass and random-bond ferromagnetic phases, the sweep-rate scaling exponent b changes with temperature T but appears not to change with antiferromagnetic bond concentration p. By contrast, in the pure ferromagnetic phase, b does not depend on T and has a sharply different value than in the two other phases.