Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses

TL;DR

This paper investigates how different external field ramping modes affect the hysteretic response of both dense and sparse Ising spin glasses at zero temperature, revealing significant variations and a percolation transition in sparse systems.

Contribution

It introduces a comparative analysis of ramping protocols in spin glasses, highlighting the impact of ramping modes on system response and uncovering a percolation transition in sparse models.

Findings

Response varies significantly with ramping mode.

Percolation transition observed in sparse systems.

System size dependence affects traditional protocols.

Abstract

We consider the hysteretic behavior of Ising spin glasses at $T=0$ for various modes of driving. Previous studies mostly focused on an infinitely slow speed $\dot{H}$ by which the external field $H$ was ramped to trigger avalanches of spin flips by starting with destabilizing a single spin while few have focused on the effect of different driving methods. First, we show that this conventional protocol imposes a system size dependence. Then, we numerically analyze the response of Ising spin glasses at rates $\dot{H}$ that are fixed as well, to elucidate the differences in the response. Specifically, we compare three different modes of ramping ($\dot{H}=c/N$, $\dot{H}=c/\sqrt{N}$, and $\dot{H}=c$ for constant $c$) for two types of spin glass systems of size $N$, representing dense networks by the Sherrington-Kirkpatrick model and sparse networks by the lattice spin glass in $d=3$ dimensions known as the Edwards Anderson model. Depending on the mode of ramping, we find that the response of each system, in form of spin-flip avalanches and other observables, can vary considerably. In particular, in the $N$-independent mode applied to the lattice spin glass, which is closest to experimental reality, we observe a percolation transition with a broad avalanche distribution between phases of localized and system-spanning responses. We explore implications for combinatorial optimization problems pertaining to sparse systems.