Zero Droplet Stiffness Exponent $\theta$ 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: $J/r^{\sigma }$. 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.

4 pages, 2 figures