On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses

Fuente: arXiv
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Main Authors: Auffinger, Antonio, Alaoui, Ahmed El, Sellke, Mark
Format: Preprint
Published: 2025
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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