Non-Shattering at and Above the Dynamical Temperature in the Spherical Pure p-Spin Model

Excerpt

arXiv:2608.14369v1 Announce Type: cross Abstract: We consider the notion of shattering introduced by Ben Arous and Jagannath for spherical pure $p$-spin glasses with overlap $q$. For every $p\geq 3$ and $0 \sqrt{(p-2)/(p-1)}$. The proof combines a deterministic $N+1$ bound for disjoint bands in the first range with a general-$p$ sign law showing that their total marked weight has subdominant free energy in the second. A spherical-code bound and H\"older's inequality give an additional $q$-depend