FRSB in the SK spin glass: convergence to full-interval support at zero temperature

Hong-Bin Chen

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arXiv · 2607.18032

FRSB in the SK spin glass: convergence to full-interval support at zero temperature

Hong-Bin Chen

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Abstract

We prove full replica symmetry breaking for the zero-field Sherrington-Kirkpatrick model at zero temperature: the Parisi minimizer is absolutely continuous, has a smooth density, and has support $[0,1)$. At inverse temperature $\beta>1$, [arxiv.org/abs/2607.11756v3] recently proved that the Parisi measure has support $[0,q_\beta]$. Here, we show $q_\beta$ converges to $1$ as $\beta\to\infty$.

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Hong-Bin Chen. 2026-07-20. FRSB in the SK spin glass: convergence to full-interval support at zero temperature. https://arxiv.org/abs/2607.18032

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