Zero Droplet Stiffness Exponent $\theta$ is Revealed in Short Range Spin Glasses when Probed with Large Avalanches Induced by Long Range Interactions

TL;DR

This paper demonstrates that in short-range spin glasses, large avalanches induced by long-range interactions reveal a zero droplet stiffness exponent, challenging previous assumptions about the nature of excitations.

Contribution

The study shows that long-range interactions induce large avalanches in short-range spin glasses, leading to a zero droplet stiffness exponent, providing new insights into spin glass excitations.

Findings

Large avalanches occur when long-range interactions are introduced.

The droplet stiffness exponent is determined to be zero.

Long-range interactions are relevant for decay exponents less than the dimension.

Abstract

We probe the droplet excitations in short range spin glasses by adding a perturbative long range interaction that decays with distance as a power law: $J/r^{\sigma}$. It is shown that if the power law exponent $\sigma$ is smaller than the spatial dimension $d$, the perturbation induces large scale avalanches which roll until they force the system to develop a pseudo gap in the excitation spectrum of the stabilities. This makes the perturbative long range interactions relevant for $\sigma < \sigma_c = d$. The droplet theory predicts that the critical exponent $\sigma_c$ depends on the droplet stiffness exponent as $\sigma_c=d-\theta$. Combining these two results leads to a zero stiffness exponent $\theta = 0$ in the droplet theory of short range spin glasses.