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.[1] 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 $A-A_{0}$ $\sim $ $h^{b}$. 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. \newline \noindent [1] B. Y\"ucesoy and A.N. Berker, Phys. Rev. B {\bf 76}, 014417 (2007).