### Abstract

We prove the impossibility of recent attempts to decouple the Replica Symmetry Breaking (RSB) picture for finite-dimensional spin glasses from the existence of many thermodynamic (i.e., infinite-volume) pure states while preserving another signature RSB feature - space filling relative domain walls between different finite-volume states. Thus revisions of the notion of pure states cannot shield the RSB picture from the internal contradictions that rule out its physical correctness in finite dimensions at low temperature in large finite volume.

Original language | English (US) |
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Pages (from-to) | 213-244 |

Number of pages | 32 |

Journal | Journal of Statistical Physics |

Volume | 106 |

Issue number | 1-2 |

DOIs | |

State | Published - 2002 |

### Keywords

- Domain walls
- Edwards-Anderson model
- Ground states
- Incongruence
- Interfaces
- Mean-field theory
- Metastases
- Pure states
- Replica symmetry breaking
- Spin glass

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Newman, C. M., & Stein, D. L. (2002). The state(s) of Replica Symmetry Breaking: Mean field theories vs. short-ranged spin glasses.

*Journal of Statistical Physics*,*106*(1-2), 213-244. https://doi.org/10.1023/A:1013128314054