Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 163, Issue 5, Pages 1069-1078Publisher
SPRINGER
DOI: 10.1007/s10955-016-1516-x
Keywords
Spin glasses; Edwards-Anderson model; Energy; Variance bounds
Categories
Funding
- NSF [DMS-1513441]
- PSC-CUNY Research Award [68784-00 46]
- U.S. NSF [DMS-1207678, DMS-131271, DMS-1440140]
- John Simon Guggenheim Foundation Fellowship
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1513441, 1312711] Funding Source: National Science Foundation
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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.
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