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

Antonio Auffinger; Ahmed El Alaoui; Mark Sellke

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arXiv · 2506.02238

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

Antonio Auffinger·Ahmed El Alaoui·Mark Sellke

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Abstract

We show that in mean-field spin glasses, a discontinuous breaking of replica symmetry at the critical inverse temperature $\beta_c$ 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 $\beta_c$.

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Antonio Auffinger, Ahmed El Alaoui, Mark Sellke. 2025-06-02. On the Discontinuous Breaking of Replica Symmetry and Shattering in Mean-Field Spin Glasses. https://arxiv.org/abs/2506.02238

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