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

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

2009-03-25

arxiv.org/abs/0903.4235v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

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.

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