Field-Driven Hysteresis of the d=3 Ising Spin Glass: Hard-Spin Mean-Field Theory

TL;DR

This paper investigates hysteresis behavior in a three-dimensional Ising spin glass using a hard-spin mean-field approach, revealing phase-dependent scaling of hysteresis loop area with sweep rate and temperature.

Contribution

It introduces a field-driven mean-field theory for spin-glass hysteresis and uncovers phase-specific scaling laws and their dependence on temperature and bond disorder.

Findings

Hysteresis loop area scales with sweep rate as A-A_0 = h^b.

The exponent b varies with temperature in spin-glass and ferromagnetic phases.

In the pure ferromagnetic phase, b is independent of temperature and differs from other phases.

Abstract

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-A_0 = 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.