Zero-Temperature Fluctuations in Short-Range Spin Glasses

TL;DR

This paper proves that energy fluctuations between certain ground states in the d-dimensional Edwards-Anderson spin glass grow proportionally with volume, using excitation metastates, and discusses implications for ground state structures.

Contribution

It establishes a lower bound on energy difference variance in spin glasses and introduces the use of excitation metastates for this analysis.

Findings

Variance of energy difference grows at least linearly with volume in dimensions ≥ 2.

Results restrict possible ground state structures in 2D spin glasses.

Uses excitation metastates as a key analytical tool.

Abstract

We consider the energy difference restricted to a finite volume for certain pairs of incongruent ground states (if they exist) in the d-dimensional Edwards-Anderson (EA) Ising spin glass at zero temperature. We prove that the variance of this quantity with respect to the couplings grows at least proportionally to the volume in any dimension greater than or equal to two. An essential aspect of our result is the use of the excitation metastate. As an illustration of potential applications, we use this result to restrict the possible structure of spin glass ground states in two dimensions.