### Abstract

We present a detailed proof of a previously announced result [1] supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on Z^{2} are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show -much less likely in our opinion - that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.

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

Pages (from-to) | 205-218 |

Number of pages | 14 |

Journal | Communications in Mathematical Physics |

Volume | 224 |

Issue number | 1 |

State | Published - 2001 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*Communications in Mathematical Physics*,

*224*(1), 205-218.

**Are there incongruent ground states in 2D Edwards-Anderson spin glasses?** / Newman, Charles; Stein, D. L.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 224, no. 1, pp. 205-218.

}

TY - JOUR

T1 - Are there incongruent ground states in 2D Edwards-Anderson spin glasses?

AU - Newman, Charles

AU - Stein, D. L.

PY - 2001

Y1 - 2001

N2 - We present a detailed proof of a previously announced result [1] supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on Z2 are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show -much less likely in our opinion - that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.

AB - We present a detailed proof of a previously announced result [1] supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin glasses (with zero external field and, e.g., Gaussian couplings): if two ground state pairs (chosen from metastates with, e.g., periodic boundary conditions) on Z2 are distinct, then the dual bonds where they differ form a single doubly-infinite, positive-density domain wall. It is an open problem to prove that such a situation cannot occur (or else to show -much less likely in our opinion - that it indeed does happen) in these models. Our proof involves an analysis of how (infinite-volume) ground states change as (finitely many) couplings vary, which leads us to a notion of zero-temperature excitation metastates, that may be of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=0035539931&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035539931&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035539931

VL - 224

SP - 205

EP - 218

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -