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We consider the energy difference restricted to a finite volume for certainpairs of incongruent ground states (if they exist) in the d-dimensionalEdwards-Anderson (EA) Ising spin glass at zero temperature. We prove that thevariance of this quantity with respect to the couplings grows at leastproportionally to the volume in any dimension greater than or equal to two. Anessential aspect of our result is the use of the excitation metastate. As anillustration of potential applications, we use this result to restrict thepossible structure of spin glass ground states in two dimensions.

Zero-Temperature Fluctuations in Short-Range Spin Glasses