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

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: $J/r^σ$. It is shown that if the power law exponent $σ$ 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 $σ< σ_c = d$. The droplet theory predicts that the critical exponent $σ_c$ depends on the droplet stiffness exponent as $σ_c=d-θ$. Combining these two results leads to a zero stiffness exponent $θ= 0$ in the droplet theory of short range spin glasses.