On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916774664994816 |
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| author | Auffinger, Antonio Alaoui, Ahmed El Sellke, Mark |
| author_facet | Auffinger, Antonio Alaoui, Ahmed El Sellke, Mark |
| contents | We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature $β_c$ implies the existence of an intermediate shattered phase. This confirms a prediction from physics regarding the nature of random first order phase transitions. On the other hand, we give an example of a spherical spin glass which exhibits shattering, yet the transition is continuous at $β_c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses Auffinger, Antonio Alaoui, Ahmed El Sellke, Mark Probability Disordered Systems and Neural Networks Mathematical Physics We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature $β_c$ implies the existence of an intermediate shattered phase. This confirms a prediction from physics regarding the nature of random first order phase transitions. On the other hand, we give an example of a spherical spin glass which exhibits shattering, yet the transition is continuous at $β_c$. |
| title | On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses |
| topic | Probability Disordered Systems and Neural Networks Mathematical Physics |
| url | https://arxiv.org/abs/2506.02238 |