## 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) |
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Pages (from-to) | 205-218 |

Number of pages | 14 |

Journal | Communications In Mathematical Physics |

Volume | 224 |

Issue number | 1 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics