### 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 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1019-1043 |

Number of pages | 25 |

Journal | Communications In Mathematical Physics |

Volume | 367 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2019 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

^{d}

*Communications In Mathematical Physics*,

*367*(3), 1019-1043. https://doi.org/10.1007/s00220-019-03418-3

**
A Relation Between Disorder Chaos and Incongruent States in Spin Glasses on Z
^{d}
.** / Arguin, L. P.; Newman, Charles; Stein, D. L.

Research output: Contribution to journal › Article

^{d}',

*Communications In Mathematical Physics*, vol. 367, no. 3, pp. 1019-1043. https://doi.org/10.1007/s00220-019-03418-3

^{d}Communications In Mathematical Physics. 2019 May 1;367(3):1019-1043. https://doi.org/10.1007/s00220-019-03418-3

}

TY - JOUR

T1 - A Relation Between Disorder Chaos and Incongruent States in Spin Glasses on Z d

AU - Arguin, L. P.

AU - Newman, Charles

AU - Stein, D. L.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=85064339383&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064339383&partnerID=8YFLogxK

U2 - 10.1007/s00220-019-03418-3

DO - 10.1007/s00220-019-03418-3

M3 - Article

VL - 367

SP - 1019

EP - 1043

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -