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A Relation Between Disorder Chaos and Incongruent States in Spin Glasses on $${\mathbb{Z}^d}$$ Z d

A Relation Between Disorder Chaos and Incongruent States in Spin Glasses on $${\mathbb{Z}^d}$$ Z d We derive lower bounds for the variance of the difference of energies between incongruent ground states, i.e., states with edge overlaps strictly less than one, of the Edwards–Anderson model on $${\mathbb{Z}^d}$$ Z d . The bounds highlight a relation between the existence of incongruent ground states and the absence of edge disorder chaos. In particular, it suggests that the presence of disorder chaos is necessary for the variance to be of order less than the volume. In addition, a relation is established between the scale of disorder chaos and the size of critical droplets. The results imply a long-conjectured relation between the droplet theory of Fisher and Huse and the absence of incongruence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

A Relation Between Disorder Chaos and Incongruent States in Spin Glasses on $${\mathbb{Z}^d}$$ Z d

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References (39)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
DOI
10.1007/s00220-019-03418-3
Publisher site
See Article on Publisher Site

Abstract

We derive lower bounds for the variance of the difference of energies between incongruent ground states, i.e., states with edge overlaps strictly less than one, of the Edwards–Anderson model on $${\mathbb{Z}^d}$$ Z d . The bounds highlight a relation between the existence of incongruent ground states and the absence of edge disorder chaos. In particular, it suggests that the presence of disorder chaos is necessary for the variance to be of order less than the volume. In addition, a relation is established between the scale of disorder chaos and the size of critical droplets. The results imply a long-conjectured relation between the droplet theory of Fisher and Huse and the absence of incongruence.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Apr 6, 2019

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