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 Ising spin glass at zero temperature. We prove that the variance of this quantity with respect to the couplings grows proportionally to the volume in any d≥ 2. 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.
Original language | English (US) |
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Pages (from-to) | 1069-1078 |
Number of pages | 10 |
Journal | Journal of Statistical Physics |
Volume | 163 |
Issue number | 5 |
DOIs | |
State | Published - Jun 1 2016 |
Keywords
- Edwards–Anderson model
- Energy
- Spin glasses
- Variance bounds
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics