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

TL;DR

This study explores how the hysteresis area in a 3D $ ext{±}J$ Ising spin glass scales with bond randomness, temperature, and sweep rate, revealing universal power-law behaviors and dynamic regimes.

Contribution

It introduces a comprehensive analysis of hysteresis area scaling in the 3D $ ext{±}J$ Ising spin glass across the entire spin-glass phase using frustration-preserving mean field theory.

Findings

Hysteresis area exhibits power-law scaling with bond randomness and temperature.

Two dynamic regimes are identified separated by a threshold frequency.

Hysteresis area remains constant below the threshold frequency and increases above it.

Abstract

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.