Zero-Temperature Fluctuations in Short-Range Spin Glasses
Mathematical Physics
2016-05-04 v2 Disordered Systems and Neural Networks
math.MP
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.
Keywords
Cite
@article{arxiv.1601.07933,
title = {Zero-Temperature Fluctuations in Short-Range Spin Glasses},
author = {L. -P. Arguin and C. M. Newman and D. L. Stein and J. Wehr},
journal= {arXiv preprint arXiv:1601.07933},
year = {2016}
}
Comments
9 pages. arXiv admin note: text overlap with arXiv:1403.1208