Zero Droplet Stiffness Exponent: Probing Short Range Spin Glasses with Avalanches Induced by Long Range Interactions

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.