## Abstract

Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated with leaves of a tree, and the Euclidean distance between them corresponds to the distance along this tree. We survey recent progress toward a rigorous proof of this picture in the context of mixed p-spin spin glass models. We focus in particular on the following topics: (i) The structure of critical points of the Hamiltonian; (ii) The realization of the ultrametric tree as near optima of a suitable TAP free energy; (iii) The construction of an efficient optimization algorithm that exploits this picture.

Original language | English (US) |
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Title of host publication | Spin Glass Theory and Far Beyond |

Subtitle of host publication | Replica Symmetry Breaking after 40 Years |

Publisher | World Scientific Publishing Co. |

Pages | 609-633 |

Number of pages | 25 |

ISBN (Electronic) | 9789811273926 |

ISBN (Print) | 9789811273919 |

DOIs | |

State | Published - Jan 1 2023 |

## ASJC Scopus subject areas

- General Engineering
- General Physics and Astronomy